id
string | setting_key
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|
algebra_func_area_train_0600
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-1(-2sin(3πx + 2) - 3)^2 + 5(-2sin(3πx + 2) - 3) + 4) - 2 and g(x) = 4(-4x + 1)^2 + 2(-4x + 1) from x = 0.8 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0601
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-5(3|x - 1| - 3) - 3)^2 - 1(-5(3|x - 1| - 3) - 3) + 2 and g(x) = 3|(3x^2 + 2) - 1| between the vertical lines x = 1.6 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0602
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(2cos(2π(-1|(-3x - 1) + 3| + 3) + 2) - 3)^2 - 3(2cos(2π(-1|(-3x - 1) + 3| + 3) + 2) - 3) + 5 and g(x) = 1|((-1(2cos(2πx - 2) + 1) + 3)/(1(2cos(2πx - 2) + 1) + 3)) - 2| + 1 from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0603
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(1(3((3x - 2)/(2x + 2)) - 2)^2 - 4) + 2| + 2, g(x) = -1sin(2π(3((1x + 3)/(1x))^2 + 1((1x + 3)/(1x)) - 2) + 1) - 1, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0604
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(1|(-2(1x^2 + 5x + 2) - 5)| - 3) - 3)/(-1(1|(-2(1x^2 + 5x + 2) - 5)| - 3) + 2), g(x) = 2e^(-2((1(2x - 5) + 2)/(-1(2x - 5) + 2))) + 1, x = -4.5, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0605
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-2|(1cos(1π(3x^2 + 3x - 3) + 1))|) + 2)/(-1(-2|(1cos(1π(3x^2 + 3x - 3) + 1))|)) and g(x) = -4((-1(1|x + 2|) - 2)/(-2(1|x + 2|) - 3)) + 3 from x = -1.0 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0606
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1e^(1(3|x + 3| + 1)) + 2 and g(x) = -1x^2 - 4x - 5 from x = -3.2 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0607
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2(2cos(1π(-2x^2 - 4x - 2) + 1) - 1) - 4) - 1)/(3(-2(2cos(1π(-2x^2 - 4x - 2) + 1) - 1) - 4) - 2) and g(x) = -1|((-3(5x^2 + 4x - 3) + 2)/(-1(5x^2 + 4x - 3) - 2))| - 2 between the vertical lines x = 0.7 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0608
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(-1x^2 + 1x + 2) - 2) - 2 and g(x) = -1|x + 3| + 1 between the vertical lines x = 1.1 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.6
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0609
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(-2cos(3πx + 3) - 3) + 5 and g(x) = -3x^2 + 3x - 3 from x = -0.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.6
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0610
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(2sin(1πx + 1) + 3) + 1)/(-3(2sin(1πx + 1) + 3) + 2) and g(x) = -3|x - 3| from x = 2.7 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0611
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3cos(2πx) - 2) + 2)/(2(-3cos(2πx) - 2) - 3), g(x) = -5x^2 + 1, x = -0.6, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0612
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4((-3(-3(3|x + 3| + 3)^2 - 4) - 1)/(1(-3(3|x + 3| + 3)^2 - 4) - 3)) + 3 and g(x) = -2|(-1((1x + 2)/(3x + 1)))| + 3 from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0613
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4((-2x - 2)/(1x + 2))^2 + 2((-2x - 2)/(1x + 2)) - 2 and g(x) = 3x^2 + 2x + 5 from x = -3.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-45.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0614
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(-1cos(2π(-1x - 3) + 2)) - 2| + 2) - 3)/(2(1|(-1cos(2π(-1x - 3) + 2)) - 2| + 2) - 1) and g(x) = 1((2(-5x^2 + 1x + 5) - 3)/(-1(-5x^2 + 1x + 5) - 3)) + 5 from x = -1.3 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
44.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0615
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3π(-5x - 2) + 2) - 3 and g(x) = 3x + 3 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0616
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3cos(1π(-5x - 5) - 3) + 1) - 2)/(2(-3cos(1π(-5x - 5) - 3) + 1) - 1) and g(x) = -2e^(-1((3x - 3)/(2x))) + 1 between the vertical lines x = -2.7 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0617
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (3(1(-1|x - 1| - 1) + 5) + 3)/(1(1(-1|x - 1| - 1) + 5)) and g(x) = 5(-2cos(2πx - 1))^2 - 2(-2cos(2πx - 1)) + 1 from x = 2.0 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0618
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3x + 3)^2 + 3(-3x + 3) - 5 and g(x) = -3x - 2 between the vertical lines x = 1.0 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0619
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(3πx)) - 1)/(-3(-1cos(3πx))) and g(x) = 3x - 3 from x = -0.8 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0620
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(2π(4(1|(-4x^2 - 2x + 4)|) + 5) - 1) and g(x) = (3(5(1|x - 3| + 1) - 1) - 3)/(1(5(1|x - 3| + 1) - 1) + 3) from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0621
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(-2sin(1πx + 1) + 1)^2 - 5, g(x) = 1x^2 - 4, x = 3.6, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0622
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-5(5(-2|x - 3| + 3)^2 - 1(-2|x - 3| + 3) - 1) + 3))/(-3(-5(5(-2|x - 3| + 3)^2 - 1(-2|x - 3| + 3) - 1) + 3) - 3) and g(x) = (-2(-4(-1|x - 1| - 2) + 2))/(3(-4(-1|x - 1| - 2) + 2) - 2) between the vertical lines x = 1.1 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0623
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -5(-2x - 4)^2 + 5(-2x - 4) + 1 and g(x) = -3|x + 2| - 1 from x = -2.8 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.6
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0624
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2x - 3) + 1| + 2 and g(x) = (1x)/(-2x - 1) between the vertical lines x = -0.6 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0625
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1cos(2πx - 2) + 3) + 5 and g(x) = -2x - 3 between the vertical lines x = 3.0 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0626
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π((-1(4x + 2) + 3)/(3(4x + 2))) - 3) - 1 and g(x) = 3sin(2π(-3x + 4) - 3) - 2 from x = 0.5 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0627
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1cos(3π(-2|((-1x)/(1x)) + 3| + 2) + 2) + 1, g(x) = (2(1x^2 - 5x - 2) + 3)/(2(1x^2 - 5x - 2) + 2), x = 0.0, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0628
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-1|(-3x - 2)| - 3) - 2)/(3(-1|(-3x - 2)| - 3) + 3), g(x) = -1|(3sin(2πx + 2) + 3) - 2|, x = -4.7, and x = -4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0629
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-1(3x - 3)^2 - 1(3x - 3)) - 3)/(-1(-1(3x - 3)^2 - 1(3x - 3)) + 3), g(x) = 3(-1|x - 1| + 1) + 5, x = -2.6, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
36.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0630
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|((1(5(-4x + 1)^2 - 2(-4x + 1) - 4) - 2)/(-1(5(-4x + 1)^2 - 2(-4x + 1) - 4) - 3)) - 1| - 3 and g(x) = (2(-2(2cos(1πx - 1) + 3) - 4) + 2)/(3(-2(2cos(1πx - 1) + 3) - 4) - 2) from x = 0.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0631
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(3e^(1(2|x + 3| - 1)) - 2) - 2 and g(x) = 2cos(1π((1x + 1)/(1x - 2)) + 3) - 2 from x = -3.4 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0632
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 4(-2sin(2π(1x - 4)) + 1)^2 - 4(-2sin(2π(1x - 4)) + 1) + 2, g(x) = 1sin(2π((-3x - 1)/(-3x + 2)) + 3) + 1, x = 1.1, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.8
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0633
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-5(1|x - 3| + 2) - 3) + 2)/(-3(-5(1|x - 3| + 2) - 3) - 3), g(x) = -2cos(1π(2x - 4) - 2), x = -0.3, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0634
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|(-3sin(2πx + 1) + 3) - 1| and g(x) = 5x + 2 from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0635
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(2sin(2πx + 3)) - 1)/(3(2sin(2πx + 3)) - 1) and g(x) = (3x - 3)/(-3x + 2) from x = -3.0 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0636
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(-2((3x + 1)/(1x + 2)) + 3)^2 + 1(-2((3x + 1)/(1x + 2)) + 3) - 2 and g(x) = (3(2sin(2πx - 1) - 1) + 1)/(-2(2sin(2πx - 1) - 1) + 3) from x = 2.6 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0637
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2sin(1πx + 2) + 1)^2 - 3(-2sin(1πx + 2) + 1) + 1 and g(x) = 4x^2 + 5x - 5 between the vertical lines x = -1.7 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0638
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2cos(3πx + 2) - 1) + 1 and g(x) = (2x + 1)/(2x + 1) from x = -4.0 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0639
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((2(-2|x + 2| - 2) + 1)/(3(-2|x + 2| - 2) + 2)) + 3, g(x) = -3(2sin(2πx) + 1), x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0640
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2e^(-1x) - 2)^2 - 1(2e^(-1x) - 2) - 3 and g(x) = -1x^2 + 2x + 2 between the vertical lines x = -0.4 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0641
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-3(-1|x + 1| - 3))/(-3(-1|x + 1| - 3) - 3))^2 + 1((-3(-1|x + 1| - 3))/(-3(-1|x + 1| - 3) - 3)) + 2 and g(x) = 3cos(3π((2x - 1)/(1x + 3)) + 3) between the vertical lines x = 2.1 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0642
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(1cos(1πx - 2) - 2)^2 - 5(1cos(1πx - 2) - 2) + 5, g(x) = 3x^2 - 1x + 5, x = 3.1, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0643
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1x^2 + 3x - 2) - 2 and g(x) = 1x + 3 between the vertical lines x = -0.6 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0644
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2((-1(1(2|x - 3| + 1) - 5) - 1)/(1(1(2|x - 3| + 1) - 5)))^2 + 5((-1(1(2|x - 3| + 1) - 5) - 1)/(1(1(2|x - 3| + 1) - 5))) + 2 and g(x) = -4(2sin(2π((-2x + 2)/(-3x)) + 1) + 2)^2 - 1(2sin(2π((-2x + 2)/(-3x)) + 1) + 2) + 1 from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0645
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2sin(2π((2(-4(-2|x + 3| + 1) - 4) - 1)/(2(-4(-2|x + 3| + 1) - 4) + 1)) + 2) - 2 and g(x) = -1cos(1π(1|((-1x - 1)/(-1x - 2)) - 3| + 3) + 3) from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0646
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2|((1(4x + 3) - 1)/(2(4x + 3) + 1)) + 2| + 2)^2 + 4(-2|((1(4x + 3) - 1)/(2(4x + 3) + 1)) + 2| + 2) + 1 and g(x) = 1cos(3π(-1(5x + 2)^2 + 2(5x + 2) + 4) - 1) + 2 between the vertical lines x = -0.8 and x = -0.7000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0647
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1(-3|(3x^2 - 2x - 1) + 2| - 2) - 5) - 2)/(-3(-1(-3|(3x^2 - 2x - 1) + 2| - 2) - 5) + 2) and g(x) = 2sin(2π((1(3x) - 1)/(2(3x) + 2)) - 1) + 3 between the vertical lines x = -0.1 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0648
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2(-3|((-1x - 1)/(-3x + 1)) + 3|)^2 + 5(-3|((-1x - 1)/(-3x + 1)) + 3|) - 1) + 4 and g(x) = 3(3(-2cos(1πx - 3) - 1)^2 - 5(-2cos(1πx - 3) - 1) + 2) - 2 between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0649
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(1((3(2cos(3πx - 1) - 3) - 3)/(-3(2cos(3πx - 1) - 3) + 4)) + 4) - 2| - 2 and g(x) = 1(1|((1x - 2)/(-3x + 2)) + 2| + 2)^2 - 3(1|((1x - 2)/(-3x + 2)) + 2| + 2) - 4 between the vertical lines x = -0.5 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0650
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3cos(3πx + 1) - 3) + 2 and g(x) = 3|x - 3| - 2 between the vertical lines x = 3.0 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0651
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3|((2(1x^2 + 5x + 2) + 1)/(1(1x^2 + 5x + 2) + 3)) - 1| - 3) + 2 and g(x) = (-3(1cos(1π(-1x^2) - 1) - 2))/(-2(1cos(1π(-1x^2) - 1) - 2) - 3) between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0652
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-5(-5x^2 + 1x + 4) - 1) - 3)/(-1(-5(-5x^2 + 1x + 4) - 1) - 3) and g(x) = -2e^(-1(-2x^2 - 3x + 2)) + 3 from x = 0.7 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0653
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π(-1|((2x)/(2x - 1)) + 1| - 3) + 3) + 3 and g(x) = -2|(3e^(2x) - 2) + 2| + 2 between the vertical lines x = -4.2 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0654
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(2x^2 + 3x - 1)), g(x) = (-2x + 1)/(-2x - 1), x = 1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0655
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(1x + 5) - 3)/(-2(1x + 5) + 3))^2 + 2((-3(1x + 5) - 3)/(-2(1x + 5) + 3)) - 3 and g(x) = 5(1|x| - 1)^2 + 5(1|x| - 1) - 4 between the vertical lines x = -0.6 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0656
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(-3sin(2π(-5x^2 - 1x + 2) + 1) - 1) + 5, g(x) = -3cos(2π(-2x^2 + 5x - 3) + 1) + 1, x = 4.0, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0657
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(4(-3e^(2((1x - 1)/(-3x + 2)))) + 1)| and g(x) = (2(5(2x + 3)^2 + 1(2x + 3) + 2) - 2)/(3(5(2x + 3)^2 + 1(2x + 3) + 2) - 2) from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0658
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1e^(1(-5x - 2)) - 1, g(x) = -3x^2 - 2x + 1, x = -0.6, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0659
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-4(1cos(1π(4x - 2)) - 3)^2 + 1(1cos(1π(4x - 2)) - 3) + 4) + 1)/(2(-4(1cos(1π(4x - 2)) - 3)^2 + 1(1cos(1π(4x - 2)) - 3) + 4)), g(x) = (-3(-1|(-2e^(2x) + 3) + 2|) - 1)/(2(-1|(-2e^(2x) + 3) + 2|) + 1), x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0660
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2((-3(-1cos(1π(-1|x + 1| - 2) + 3) - 2) + 2)/(3(-1cos(1π(-1|x + 1| - 2) + 3) - 2) - 2))^2 + 1((-3(-1cos(1π(-1|x + 1| - 2) + 3) - 2) + 2)/(3(-1cos(1π(-1|x + 1| - 2) + 3) - 2) - 2)) - 2 and g(x) = -5(-3|(-2x + 4) + 3| + 3)^2 + 5(-3|(-2x + 4) + 3| + 3) - 1 from x = 3.2 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0661
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(2(-3e^(-2(-4x^2 + 4x + 3))) + 2) - 3)/(-1(2(-3e^(-2(-4x^2 + 4x + 3))) + 2) + 2), g(x) = -1((-1(-2|x - 2| + 1) + 3)/(-3(-2|x - 2| + 1) + 2))^2 + 5((-1(-2|x - 2| + 1) + 3)/(-3(-2|x - 2| + 1) + 2)) + 4, x = 1.8, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
-6.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0662
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(3(-2e^(1(3x + 2)) + 3)^2 + 4(-2e^(1(3x + 2)) + 3) - 4) - 2| + 3, g(x) = (-2(-3|(-3e^(-2x) + 1) + 1| - 3) + 2)/(-1(-3|(-3e^(-2x) + 1) + 1| - 3) + 2), x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0663
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|((-2x - 3)/(2x - 3)) - 3| + 2 and g(x) = -1x^2 - 4x + 2 from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.8
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0664
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(2|(2sin(3π(5x - 3) - 1) - 2) - 1|) + 3)/(-2(2|(2sin(3π(5x - 3) - 1) - 2) - 1|) - 2), g(x) = -1sin(1π(-4((1x - 1)/(2x - 1)) - 4) + 3), x = 2.6, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0665
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-4(1((-1x + 3)/(-3x - 1)) - 3)^2 - 1(1((-1x + 3)/(-3x - 1)) - 3) + 3) + 3| + 2 and g(x) = -3cos(2π(-5((2x)/(-1x - 1)) + 2) + 3) between the vertical lines x = -1.4 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0666
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(3(-1(2|x|) + 5)^2 - 5(-1(2|x|) + 5) - 1) - 3)/(-1(3(-1(2|x|) + 5)^2 - 5(-1(2|x|) + 5) - 1)) and g(x) = -5((-2(-3x - 5) + 3)/(2(-3x - 5) + 2))^2 - 1((-2(-3x - 5) + 3)/(2(-3x - 5) + 2)) + 3 between the vertical lines x = -2.6 and x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0667
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(3(-3|(-3e^(-2x) + 2) - 2| + 3) + 3)^2 + 5(3(-3|(-3e^(-2x) + 2) - 2| + 3) + 3) - 3 and g(x) = 1(-1cos(2π((2x + 3)/(-3x + 1)) + 1) + 2)^2 + 1(-1cos(2π((2x + 3)/(-3x + 1)) + 1) + 2) - 5 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0668
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2|(4((3(4x^2 - 1x - 3) + 2)/(1(4x^2 - 1x - 3) + 2)) + 2) + 2| + 1, g(x) = 2(2sin(3π(-1|x - 1|) + 3) + 2), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0669
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|(1x - 2)|) + 3)/(-3(-1|(1x - 2)|) + 4) and g(x) = -3sin(1π(1|x + 1| + 3)) from x = 3.1 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0670
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(-1(-2cos(1πx + 1) + 2)^2 + 3(-2cos(1πx + 1) + 2) + 1) + 4) - 2)/(-1(3(-1(-2cos(1πx + 1) + 2)^2 + 3(-2cos(1πx + 1) + 2) + 1) + 4) + 2) and g(x) = 1((-3(-2x^2 - 2x + 4) - 3)/(2(-2x^2 - 2x + 4) + 1)) - 5 between the vertical lines x = 2.9 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0671
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3(-2|((-2(5x - 4))/(-1(5x - 4) + 3)) + 3| + 3)^2 - 4(-2|((-2(5x - 4))/(-1(5x - 4) + 3)) + 3| + 3) - 3, g(x) = -2sin(2π(1|((1x + 2)/(1x - 3))| - 2)) + 2, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0672
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(-1(3(3e^(-1x) - 3) - 1)^2 - 4) + 2| and g(x) = (-2(-3cos(2π(2|x + 3|) - 3) - 1) + 3)/(-1(-3cos(2π(2|x + 3|) - 3) - 1) - 2) from x = 1.1 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
29.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0673
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5(-2|(1((2x - 1)/(1x + 2))^2 + 3((2x - 1)/(1x + 2)) - 2) + 2| + 3) - 4 and g(x) = (-1(1(4x^2 - 4x) + 1) - 3)/(-2(1(4x^2 - 4x) + 1) - 2) from x = -1.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0674
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3cos(1πx + 1))^2 + 5(-3cos(1πx + 1)) - 1 and g(x) = -4x^2 + 1x + 4 between the vertical lines x = -0.6 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0675
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(4((3(-1x^2 - 2x - 2))/(-1(-1x^2 - 2x - 2) - 3)) - 4) - 1| - 2 and g(x) = (1(-4(3cos(3πx) - 1) + 3) + 3)/(-1(-4(3cos(3πx) - 1) + 3) + 3) between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0676
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3cos(2πx + 3) + 3)^2 - 3(-3cos(2πx + 3) + 3) and g(x) = 1x^2 - 3x - 2 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0677
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1x^2 - 4x + 2) + 2 and g(x) = 1|x + 2| - 1 between the vertical lines x = 0.6 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21.9
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0678
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π(3((1x - 2)/(-1x))^2 - 5((1x - 2)/(-1x)) - 5) + 2), g(x) = 2cos(1π(2|x + 2| - 2) + 1) + 1, x = -0.5, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0679
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(1sin(3πx - 2) + 2)^2 + 4(1sin(3πx - 2) + 2) - 5) + 2)/(2(-5(1sin(3πx - 2) + 2)^2 + 4(1sin(3πx - 2) + 2) - 5) - 1) and g(x) = 5(3sin(3πx - 1) - 1) - 2 between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0680
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2(-2((-1x + 1)/(-3x))^2) + 3, g(x) = (-1(-1x - 4) - 2)/(2(-1x - 4) + 2), x = -2.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.5
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0681
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|(-2(-3cos(1π((-1x - 2)/(-3x + 1)) + 2)) + 1)| - 1, g(x) = (-1(-2(-2x + 2)^2 - 3(-2x + 2) - 5) + 3)/(1(-2(-2x + 2)^2 - 3(-2x + 2) - 5)), x = 0.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0682
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|(3cos(2πx + 2) + 2)| + 3, g(x) = -1x^2 - 2, x = -1.1, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.7
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0683
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(3π(2(-2|x + 3| - 2) - 5)) - 1)^2 - 2(-1sin(3π(2(-2|x + 3| - 2) - 5)) - 1) + 2 and g(x) = (2(-2|(-5x^2 + 4x + 1) + 2|) + 3)/(-2(-2|(-5x^2 + 4x + 1) + 2|) + 3) between the vertical lines x = 0.7 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0684
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(-4(-2((-2x + 1)/(3x)) - 3)^2 + 2(-2((-2x + 1)/(3x)) - 3) + 3) + 1| - 3 and g(x) = -2((-1(3|x + 2| + 1) - 2)/(2(3|x + 2| + 1) - 1))^2 + 4 from x = -0.3 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0685
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(-5x - 2)^2 + 1(-5x - 2) + 1) - 3)/(-3(-3(-5x - 2)^2 + 1(-5x - 2) + 1) - 3) and g(x) = 2(2e^(1x) + 2) from x = -0.6 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0686
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3|(4x - 2) - 2| + 2)^2 - 3(3|(4x - 2) - 2| + 2) + 3 and g(x) = 3sin(2π((-3x + 1)/(2x - 3)) + 2) + 1 between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0687
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1sin(1π(-4(-4((-1x + 2)/(3x - 2)) - 4)^2 + 3(-4((-1x + 2)/(3x - 2)) - 4) + 3) + 3) + 2 and g(x) = -2sin(3π(4(1|x + 1| + 2)^2 + 3(1|x + 1| + 2) - 2) + 3) + 2 from x = -4.2 to x = -4.1000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0688
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(3(-2cos(2πx + 1) - 1) + 5) + 2)/(1(3(-2cos(2πx + 1) - 1) + 5) + 3) and g(x) = (2(-1cos(3πx - 2)) - 3)/(1(-1cos(3πx - 2)) + 2) from x = 4.7 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0689
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(5x)| and g(x) = -1|x - 1| between the vertical lines x = -0.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0690
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-4x - 3) + 1)/(-1(-4x - 3)), g(x) = 3x + 2, x = -0.9, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0691
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3x^2 - 3x - 2) + 4 and g(x) = -3x - 4 between the vertical lines x = -0.9 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0692
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-3|x - 3| + 2) + 3)/(2(-3|x - 3| + 2) + 1) and g(x) = 5x - 2 from x = 0.6 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
22.1
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0693
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(-2|x - 3| + 2) - 2) - 1 and g(x) = (3x + 2)/(-2x - 2) from x = -4.4 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.3
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0694
|
algebra_func_area
|
[
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2sin(2π((-3x - 1)/(-1x - 1))), g(x) = -4x + 1, x = 0.4, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0695
|
algebra_func_area
|
[
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2|x|)^2 - 3(-2|x|) + 5 and g(x) = 5x^2 + 4x + 4 from x = -1.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.6
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0696
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1cos(2πx + 2) + 1) - 4 and g(x) = -3|x + 3| + 3 between the vertical lines x = -0.1 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.0
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0697
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(4(-4((1x)/(-1x + 3))^2 + 3((1x)/(-1x + 3)) + 4)) + 2| - 1 and g(x) = (1(3|(1x^2) - 2| + 1) - 3)/(2(3|(1x^2) - 2| + 1) - 1) between the vertical lines x = 1.8 and x = 1.9000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.2
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0698
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(3|(4x^2 - 4) + 1| - 3) - 3)/(2(3|(4x^2 - 4) + 1| - 3))) + 3 and g(x) = 2(1e^(-1((-2x + 3)/(2x - 3))))^2 - 1(1e^(-1((-2x + 3)/(2x - 3)))) - 2 between the vertical lines x = -1.6 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
32.4
|
MATH_EXPLORATIVE
|
algebra_func_area_train_0699
|
algebra_func_area
|
[
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2sin(3πx)) - 1| + 1 and g(x) = -2x between the vertical lines x = -2.4 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.8
|
MATH_EXPLORATIVE
|
Subsets and Splits
Unique Ground Truths Sorted
Lists unique ground truth values from the dataset, providing basic insight into the variety of possible outcomes.
Distinct Ground Truth Values Sorted
Lists unique ground truth values from the dataset, providing a basic overview of the possible outcomes.
Ground Truth Sorted Distinctly
Lists unique ground truth values from the dataset in sorted order, providing basic insight into the variety of possible outcomes.
Unique Ground Truth Values
Lists unique ground truth values from the dataset, providing basic insight into the variety of possible outcomes.