id
stringlengths 31
70
| setting_key
stringclasses 167
values | difficulty
stringclasses 4
values | level
int32 1
7
| messages
dict | ground_truth
stringlengths 1
19
| dataset
stringclasses 1
value | omega_split
stringclasses 1
value |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_1_1_500
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(2|x + 2| - 1) + 2| - 2 and g(x) = (-2x - 1)/(-3x - 1) from x = -2.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_1_1_501
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(3x - 1) - 1) + 1 and g(x) = -1x - 1 between the vertical lines x = -2.9 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_1_1_502
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(2x^2 + 5x - 1) - 3 and g(x) = 1|x + 1| + 3 from x = -2.2 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.7
|
math
|
train
|
math_algebra_func_area_level_1_1_503
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-3|x - 1| + 3) - 1)/(3(-3|x - 1| + 3) + 2), g(x) = -2|x| - 3, x = -0.3, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.4
|
math
|
train
|
math_algebra_func_area_level_1_1_504
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(2cos(3πx + 1) - 1) + 2 and g(x) = -3x + 2 from x = -1.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_505
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1sin(3π(-2x - 2) - 1) - 1, g(x) = -4x^2 + 5x - 1, x = 1.1, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_506
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(1π(-2|x - 3|) + 3) - 2, g(x) = (-1x + 1)/(2x + 3), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.4
|
math
|
train
|
math_algebra_func_area_level_1_1_507
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((3x + 3)/(-1x - 1)) - 1)/(-1((3x + 3)/(-1x - 1)) + 2) and g(x) = 1x^2 - 1x + 1 from x = 0.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_508
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2cos(1π(1x)) + 3, g(x) = -3|x - 3| + 2, x = 2.8, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_509
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-4x^2 - 4x - 2) - 1)/(2(-4x^2 - 4x - 2)) and g(x) = -3|x - 3| + 2 between the vertical lines x = 2.0 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_1_1_510
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(1π(1x + 2) - 2) - 1 and g(x) = -2x + 2 from x = 1.7 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_1_1_511
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(5x^2 - 4x - 4) - 4 and g(x) = 1|x + 2| + 3 between the vertical lines x = -0.8 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
45.6
|
math
|
train
|
math_algebra_func_area_level_1_1_512
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-4x^2 + 5x + 1) + 2, g(x) = 2|x + 2| + 2, x = -0.5, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.3
|
math
|
train
|
math_algebra_func_area_level_1_1_513
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3|(-3x - 1) + 2| + 1 and g(x) = 1|x| + 2 between the vertical lines x = 0.2 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_514
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-3sin(2πx + 3) - 1)^2 + 5(-3sin(2πx + 3) - 1) - 2, g(x) = -1x^2 - 3x + 1, x = 1.1, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_1_1_515
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3cos(2π(-3x + 2) - 3) and g(x) = 1x^2 - 5x + 2 from x = 4.6 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_516
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(2cos(2πx) - 2) + 3| + 3, g(x) = 1|x - 1| - 3, x = 0.1, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.7
|
math
|
train
|
math_algebra_func_area_level_1_1_517
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-2cos(2πx - 1) - 1) + 1 and g(x) = (-2x + 2)/(-3x + 2) from x = 1.8 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_1_1_518
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-3cos(1πx + 3) - 2) - 1| - 3, g(x) = 3x^2 - 3x - 3, x = 0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_519
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(1πx) - 3)^2 + 2(-2sin(1πx) - 3) + 2 and g(x) = 3x + 2 between the vertical lines x = -4.8 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_1_1_520
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(1cos(1πx - 1) + 2) + 1| + 1, g(x) = 2|x - 2| + 3, x = 1.7, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_1_1_521
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1sin(2π(-1x^2 - 3x + 5) + 2) and g(x) = 3|x + 2| - 1 from x = -2.2 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_522
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3e^(-2(-4x^2 - 2x + 2)) - 3 and g(x) = -3x^2 - 1 from x = -0.8 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_1_1_523
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(1x + 3)) + 3 and g(x) = (3x - 3)/(-2x + 3) between the vertical lines x = -3.8 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.1
|
math
|
train
|
math_algebra_func_area_level_1_1_524
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(1x^2 + 3x + 1)^2 + 2(1x^2 + 3x + 1) and g(x) = -1x^2 - 5x - 4 between the vertical lines x = -2.9 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.7
|
math
|
train
|
math_algebra_func_area_level_1_1_525
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(2|x - 1| + 1) - 3)/(3(2|x - 1| + 1)), g(x) = -2|x| + 3, x = -2.1, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.6
|
math
|
train
|
math_algebra_func_area_level_1_1_526
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2|x|) - 2)/(-2(2|x|) + 3) and g(x) = -3|x + 2| - 1 from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.4
|
math
|
train
|
math_algebra_func_area_level_1_1_527
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1((-2x + 2)/(-3x + 4))^2 - 1((-2x + 2)/(-3x + 4)) - 1, g(x) = 1x^2 + 5x - 1, x = -4.8, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.2
|
math
|
train
|
math_algebra_func_area_level_1_1_528
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((1x + 1)/(3x + 2))^2 - 5((1x + 1)/(3x + 2)) + 4 and g(x) = 1|x - 3| + 3 between the vertical lines x = -0.8 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_529
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(2π((-1x + 1)/(2x + 2)) + 3) and g(x) = (-1x + 2)/(3x) from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_530
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(2cos(1πx - 2) + 1) - 3)/(2(2cos(1πx - 2) + 1) - 1) and g(x) = -1|x| + 3 between the vertical lines x = -2.5 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_531
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(1x) - 1)/(-2(1x) - 1) and g(x) = 5x^2 - 1x - 3 between the vertical lines x = -0.8 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_1_1_532
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-3cos(3πx - 3) + 2) and g(x) = 5x^2 - 3x + 1 from x = -0.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_1_1_533
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(1x + 4) - 3)/(-2(1x + 4) - 3), g(x) = (2x + 1)/(2x), x = -3.9, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.4
|
math
|
train
|
math_algebra_func_area_level_1_1_534
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2cos(2π(-2x^2 + 3x - 3) - 3), g(x) = 3|x - 2| - 2, x = 2.2, and x = 2.3000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_535
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(1sin(2πx - 3) + 3) - 1| - 2 and g(x) = 5x^2 + 3x - 2 from x = -1.5 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.6
|
math
|
train
|
math_algebra_func_area_level_1_1_536
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(2cos(1πx - 2) - 3)| + 1, g(x) = -1|x| + 3, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_537
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(3|x - 1| + 2) - 1)/(3(3|x - 1| + 2) - 2), g(x) = 2|x - 3| - 1, x = 2.3, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_1_1_538
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(-2x^2 - 2x) - 2| - 3, g(x) = 2x^2 - 4x + 3, x = -4.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.8
|
math
|
train
|
math_algebra_func_area_level_1_1_539
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-2|x + 2| + 2))/(-2(-2|x + 2| + 2) + 1) and g(x) = -1|x + 3| + 3 between the vertical lines x = -2.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.6
|
math
|
train
|
math_algebra_func_area_level_1_1_540
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-3cos(2πx + 2) - 2) + 1)/(-2(-3cos(2πx + 2) - 2) - 3) and g(x) = -2|x - 1| - 2 from x = 1.0 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_1_1_541
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((-3x + 2)/(1x - 3)) - 2)/(-1((-3x + 2)/(1x - 3)) - 2), g(x) = 3|x| - 2, x = -1.0, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_1_1_542
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(2x^2 + 5x + 4) - 3| + 1 and g(x) = 5x^2 + 5x between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_1_1_543
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-2cos(2πx + 3) - 2)^2 + 5(-2cos(2πx + 3) - 2) + 1 and g(x) = 1x + 1 from x = -4.1 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_1_1_544
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(3π(-1x + 4) + 1) - 2 and g(x) = (2x - 3)/(1x - 3) from x = 1.8 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_545
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π(2x^2 - 3x - 2) - 3) + 2 and g(x) = 2x - 2 between the vertical lines x = 2.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_546
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-2sin(3πx - 3) - 1) - 2 and g(x) = -3x^2 + 1x - 2 from x = 0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_1_1_547
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π(4x^2 - 2x + 4)) + 2 and g(x) = (-2x + 2)/(2x - 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}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_1_1_548
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π(-4x - 3) - 3) - 2 and g(x) = -3x - 1 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}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_1_1_549
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-2sin(1πx + 1) - 3)^2 + 2(-2sin(1πx + 1) - 3) - 4, g(x) = -2x - 5, x = -1.0, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_550
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3sin(3πx - 3) - 2) + 3)/(-1(-3sin(3πx - 3) - 2) - 2) and g(x) = 2x^2 - 2x + 5 from x = -4.3 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.6
|
math
|
train
|
math_algebra_func_area_level_1_1_551
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1cos(2π(3|x + 2| + 1) + 1) - 2 and g(x) = 1|x + 1| - 3 between the vertical lines x = -2.6 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_552
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π(1|x + 3| + 3) + 3) + 2 and g(x) = 1|x - 1| - 3 between the vertical lines x = -4.5 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_1_1_553
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|((-2x - 3)/(2x + 2)) - 3| - 2, g(x) = -3x + 5, x = -0.9, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.9
|
math
|
train
|
math_algebra_func_area_level_1_1_554
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(2|x - 2|)| - 1, g(x) = 1x^2 - 3x + 3, x = -2.6, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.7
|
math
|
train
|
math_algebra_func_area_level_1_1_555
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-2x^2 + 1x - 3) + 1)/(2(-2x^2 + 1x - 3)), g(x) = 4x^2 + 1x - 5, x = -1.1, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_1_1_556
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3cos(1π((2x)/(1x + 3)) - 2) and g(x) = (-1x + 3)/(2x - 1) from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_557
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-2x^2 - 3x - 2) + 3)/(-3(-2x^2 - 3x - 2) - 1) and g(x) = 1|x - 3| from x = 2.6 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_558
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-3cos(3πx - 2) - 2))/(-3(-3cos(3πx - 2) - 2) + 1) and g(x) = -2|x - 1| + 1 from x = 2.0 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_1_1_559
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(-1cos(1πx - 1) - 3) - 3 and g(x) = 2|x| - 2 between the vertical lines x = -4.2 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_1_1_560
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(3|x + 3| + 3) + 2) - 3 and g(x) = 4x^2 - 4x - 3 between the vertical lines x = 0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_1_1_561
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(-4x - 5) - 3) + 2 and g(x) = 1x between the vertical lines x = 2.6 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_562
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(3π(-2x^2 - 1x - 3) - 2) + 2, g(x) = 2|x - 3| - 3, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_563
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(1π(2x) + 1) + 3, g(x) = -4x + 5, x = 0.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_1_1_564
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(2cos(3πx + 1) + 2) + 1)/(-1(2cos(3πx + 1) + 2) + 2) and g(x) = 2x from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_565
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((-3x + 3)/(-2x + 3))^2 + 5((-3x + 3)/(-2x + 3)) - 3, g(x) = -1x^2 + 1x + 5, x = -0.6, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.2
|
math
|
train
|
math_algebra_func_area_level_1_1_566
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(2π(-3|x|) - 1) - 2, g(x) = (2x - 2)/(-1x + 3), x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_567
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(2cos(1πx) + 2) and g(x) = -3|x + 1| + 2 between the vertical lines x = 0.7 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_1_1_568
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-2x^2 - 3x) + 4, g(x) = 2|x - 1| + 1, x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.0
|
math
|
train
|
math_algebra_func_area_level_1_1_569
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-5x) - 3)/(-1(-5x) + 2), g(x) = (-3x + 1)/(2x + 1), x = -0.4, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.1
|
math
|
train
|
math_algebra_func_area_level_1_1_570
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(2cos(1πx - 1) - 1) + 2| - 1, g(x) = -5x + 5, x = 2.0, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_1_1_571
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|(-3x + 2)| + 1, g(x) = 4x + 2, x = 0.3, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_1_1_572
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(1π(-4x - 3) + 1) - 2, g(x) = -4x^2, x = -0.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_1_1_573
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-2sin(1πx + 3) + 3) - 2, g(x) = -3|x - 2| + 2, x = -0.1, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.0
|
math
|
train
|
math_algebra_func_area_level_1_1_574
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(3x - 1) + 2)/(2(3x - 1) + 2), g(x) = (1x - 3)/(-3x - 2), x = -1.9, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35.7
|
math
|
train
|
math_algebra_func_area_level_1_1_575
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-3e^(-1x) + 1) + 1 and g(x) = (-2x + 1)/(-3x + 2) from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_576
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-5x + 2) + 2)/(2(-5x + 2) + 1), g(x) = -2x - 3, x = -1.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.1
|
math
|
train
|
math_algebra_func_area_level_1_1_577
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(-1cos(1πx - 3) - 1) + 5 and g(x) = 1|x + 3| - 1 between the vertical lines x = 3.7 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_1_1_578
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1cos(1π((-3x - 1)/(-2x - 1)) + 2) + 2 and g(x) = (-1x - 3)/(-3x - 3) from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_579
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-3|x|)^2 + 1(-3|x|) - 3 and g(x) = (1x - 3)/(2x - 3) between the vertical lines x = 0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
24.5
|
math
|
train
|
math_algebra_func_area_level_1_1_580
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3|(-1e^(1x) - 1) + 1| - 2 and g(x) = (2x + 1)/(1x) between the vertical lines x = -0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
45.9
|
math
|
train
|
math_algebra_func_area_level_1_1_581
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(4x))/(2(4x) + 3), g(x) = -2|x - 2| + 2, x = 1.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_1_1_582
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(3x^2 + 5x - 4) - 5 and g(x) = (-3x - 1)/(-3x - 2) between the vertical lines x = -1.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.9
|
math
|
train
|
math_algebra_func_area_level_1_1_583
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-2sin(2πx - 1) + 2) - 5 and g(x) = (-1x)/(-1x - 2) from x = -1.2 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_584
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(2|x + 1| - 2)^2 + 2(2|x + 1| - 2) - 5 and g(x) = -1x + 3 from x = -0.9 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.1
|
math
|
train
|
math_algebra_func_area_level_1_1_585
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-3e^(-2x) + 2) - 1| + 3 and g(x) = (1x)/(-3x + 1) from x = 0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_1_1_586
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-1cos(3πx) - 3) - 1| + 2 and g(x) = 5x + 3 from x = 1.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_1_1_587
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-1x^2 + 1x + 3)| - 3 and g(x) = -4x^2 - 1x + 5 from x = -1.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.4
|
math
|
train
|
math_algebra_func_area_level_1_1_588
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3((-2x - 3)/(-3x - 2)) + 1)/(-2((-2x - 3)/(-3x - 2)) + 3) and g(x) = 2x + 5 between the vertical lines x = -2.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_1_1_589
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|((-3x + 3)/(2x - 1))| - 3 and g(x) = (-2x - 2)/(-2x - 1) between the vertical lines x = -0.8 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.4
|
math
|
train
|
math_algebra_func_area_level_1_1_590
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3((-1x - 3)/(1x + 3)) - 3)/(1((-1x - 3)/(1x + 3)) + 2), g(x) = 4x^2 + 3x - 5, x = -1.6, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.8
|
math
|
train
|
math_algebra_func_area_level_1_1_591
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(1x^2 - 1x + 2) + 3)/(-1(1x^2 - 1x + 2) - 1) and g(x) = -1x^2 + 2x + 3 from x = -1.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.8
|
math
|
train
|
math_algebra_func_area_level_1_1_592
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-3cos(3πx) - 1) - 1| + 1 and g(x) = -1x + 5 from x = 1.8 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_1_1_593
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-1x - 1) + 1, g(x) = (3x + 1)/(3x - 2), x = -0.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_1_1_594
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-2x + 2) + 1)/(-2(-2x + 2) - 3), g(x) = (2x - 2)/(-2x + 1), x = 1.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_1_1_595
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-2x^2 + 1x + 2) - 1)/(1(-2x^2 + 1x + 2)) and g(x) = -3x^2 - 1x + 4 from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_1_1_596
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-3sin(3πx + 1) - 1) - 3| - 3, g(x) = -2x^2 - 5x + 5, x = 1.9, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_1_1_597
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1sin(3πx - 1) - 1)^2 - 2(1sin(3πx - 1) - 1) - 2 and g(x) = (1x + 1)/(1x + 3) between the vertical lines x = -1.2 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_1_1_598
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(3x + 4) - 2)/(-3(3x + 4) + 1) and g(x) = (3x)/(-3x - 3) from x = -1.3 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
34.4
|
math
|
train
|
math_algebra_func_area_level_1_1_599
|
algebra_func_area1
|
easy (level 1)
| 1 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((2x - 3)/(2x + 1)) + 2)/(2((2x - 3)/(2x + 1)) - 3) and g(x) = -5x^2 + 1x + 4 from x = -0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.5
|
math
|
train
|
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