Dataset Card for numina-deepseek-r1-llama-3-70b

This dataset has been created with distilabel.

Dataset Summary

This dataset contains a pipeline.yaml which can be used to reproduce the pipeline that generated it in distilabel using the distilabel CLI:

distilabel pipeline run --config "https://huggingface.co/datasets/systemk/numina-deepseek-r1-llama-3-70b/raw/main/pipeline.yaml"

or explore the configuration:

distilabel pipeline info --config "https://huggingface.co/datasets/systemk/numina-deepseek-r1-llama-3-70b/raw/main/pipeline.yaml"

Dataset structure

The examples have the following structure per configuration:

Configuration: default

---

{
    "distilabel_metadata": {
        "raw_input_text_generation_0": null,
        "raw_output_text_generation_0": null
    },
    "generation": null,
    "messages": [
        {
            "content": "What is the coefficient of $x^2y^6$ in the expansion of $\\left(\\frac{3}{5}x-\\frac{y}{2}\\right)^8$?  Express your answer as a common fraction.",
            "role": "user"
        },
        {
            "content": "To determine the coefficient of $x^2{y}^{6}x^2y^6$ in the expansion of $left(frac35x-fracy2right{)}^8\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}x\; -\; \backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^8$, we can use the binomial theorem.\n\nThe binomial theorem states:\n\\[\n(a + b)^n = \\sum_{k=0}^{n} \\binom{n}{k} a^{n-k} b^k\n\\]\n\nIn this case, $a=frac35xa\; =\; \backslash \backslash frac\{3\}\{5\}x$, $b=-fracy2b\; =\; -\backslash \backslash frac\{y\}\{2\}$, and $n=8n\; =\; 8$.\n\nWe are interested in the term that contains $x^2{y}^{6}x^2y^6$. In the general term of the binomial expansion:\n\\[\n\\binom{8}{k} \\left(\\frac{3}{5}x\\right)^{8-k} \\left(-\\frac{y}{2}\\right)^k\n\\]\n\nTo get $x^{2}x^2$, we need $8-k=28\; -\; k\; =\; 2$, thus $k=6k\; =\; 6$.\n\nSubstituting $k=6k\; =\; 6$ into the expression:\n\\[\n\\binom{8}{6} \\left(\\frac{3}{5}x\\right)^{8-6} \\left(-\\frac{y}{2}\\right)^6 = \\binom{8}{6} \\left(\\frac{3}{5}x\\right)^2 \\left(-\\frac{y}{2}\\right)^6\n\\]\n\nNow, we will compute each part of this expression.\n\n1. Calculate the binomial coefficient $binom86\backslash \backslash binom\{8\}\{6\}$.\n2. Compute $left(frac35right{)}^2\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}\backslash \backslash right)^2$.\n3. Compute $left(-fracy2right{)}^6\backslash \backslash left(-\backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^6$.\n4. Combine everything together to get the coefficient of $x^2{y}^{6}x^2y^6$.\n\nLet\u0027s compute these in Python.\n```python\nfrom math import comb\n\n# Given values\nn = 8\nk = 6\n\n# Calculate the binomial coefficient\nbinom_coeff = comb(n, k)\n\n# Compute (3/5)^2\na_term = (3/5)**2\n\n# Compute (-1/2)^6\nb_term = (-1/2)**6\n\n# Combine terms to get the coefficient of x^2y^6\ncoefficient = binom_coeff * a_term * b_term\nprint(coefficient)\n```\n```output\n0.1575\n```\nThe coefficient of $x^2{y}^{6}x^2y^6$ in the expansion of $left(frac35x-fracy2right{)}^8\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}x\; -\; \backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^8$ is $0.15750.1575$. To express this as a common fraction, we recognize that:\n\n\\[ 0.1575 = \\frac{1575}{10000} = \\frac{63}{400} \\]\n\nThus, the coefficient can be expressed as:\n\n\\[\n\\boxed{\\frac{63}{400}}\n\\]",
            "role": "assistant"
        }
    ],
    "model_name": null,
    "problem": "What is the coefficient of $x^2y^6$ in the expansion of $\\left(\\frac{3}{5}x-\\frac{y}{2}\\right)^8$?  Express your answer as a common fraction.",
    "solution": "To determine the coefficient of $x^2{y}^{6}x^2y^6$ in the expansion of $left(frac35x-fracy2right{)}^8\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}x\; -\; \backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^8$, we can use the binomial theorem.\n\nThe binomial theorem states:\n\\[\n(a + b)^n = \\sum_{k=0}^{n} \\binom{n}{k} a^{n-k} b^k\n\\]\n\nIn this case, $a=frac35xa\; =\; \backslash \backslash frac\{3\}\{5\}x$, $b=-fracy2b\; =\; -\backslash \backslash frac\{y\}\{2\}$, and $n=8n\; =\; 8$.\n\nWe are interested in the term that contains $x^2{y}^{6}x^2y^6$. In the general term of the binomial expansion:\n\\[\n\\binom{8}{k} \\left(\\frac{3}{5}x\\right)^{8-k} \\left(-\\frac{y}{2}\\right)^k\n\\]\n\nTo get $x^{2}x^2$, we need $8-k=28\; -\; k\; =\; 2$, thus $k=6k\; =\; 6$.\n\nSubstituting $k=6k\; =\; 6$ into the expression:\n\\[\n\\binom{8}{6} \\left(\\frac{3}{5}x\\right)^{8-6} \\left(-\\frac{y}{2}\\right)^6 = \\binom{8}{6} \\left(\\frac{3}{5}x\\right)^2 \\left(-\\frac{y}{2}\\right)^6\n\\]\n\nNow, we will compute each part of this expression.\n\n1. Calculate the binomial coefficient $binom86\backslash \backslash binom\{8\}\{6\}$.\n2. Compute $left(frac35right{)}^2\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}\backslash \backslash right)^2$.\n3. Compute $left(-fracy2right{)}^6\backslash \backslash left(-\backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^6$.\n4. Combine everything together to get the coefficient of $x^2{y}^{6}x^2y^6$.\n\nLet\u0027s compute these in Python.\n```python\nfrom math import comb\n\n# Given values\nn = 8\nk = 6\n\n# Calculate the binomial coefficient\nbinom_coeff = comb(n, k)\n\n# Compute (3/5)^2\na_term = (3/5)**2\n\n# Compute (-1/2)^6\nb_term = (-1/2)**6\n\n# Combine terms to get the coefficient of x^2y^6\ncoefficient = binom_coeff * a_term * b_term\nprint(coefficient)\n```\n```output\n0.1575\n```\nThe coefficient of $x^2{y}^{6}x^2y^6$ in the expansion of $left(frac35x-fracy2right{)}^8\backslash \backslash left(\backslash \backslash frac\{3\}\{5\}x\; -\; \backslash \backslash frac\{y\}\{2\}\backslash \backslash right)^8$ is $0.15750.1575$. To express this as a common fraction, we recognize that:\n\n\\[ 0.1575 = \\frac{1575}{10000} = \\frac{63}{400} \\]\n\nThus, the coefficient can be expressed as:\n\n\\[\n\\boxed{\\frac{63}{400}}\n\\]"
}

This subset can be loaded as:

from datasets import load_dataset

ds = load_dataset("systemk/numina-deepseek-r1-llama-3-70b", "default")

Or simply as it follows, since there's only one configuration and is named default:

from datasets import load_dataset

ds = load_dataset("systemk/numina-deepseek-r1-llama-3-70b")