data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Given the parabola $C: x^{2}=2py\\left(p \\gt 0\\right)$ with focus $F$, and the minimum distance between $F$ and a point on the circle $M: x^{2}+\\left(y+4\\right)^{2}=1$ is $4$.<br/>$(1)$ Find $p$;<br/>$(2)$ If point $P$ lies on $M$, $PA$ and $PB$ are two tangents to $C$ with... | math | {
"style": "rule",
"ground_truth": "20\\sqrt{5}"
} | {
"split": "train",
"index": 40049,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f(x)=\\frac{\\cos 2x-(a+2)\\cos x+a+1}{\\sin x}.$ For constant $a$ such that $\\lim_{x\\rightarrow 0} \\frac{f(x)}{x}=\\frac 12$ , evaluate $\\int_{\\frac{\\pi}{3}}^{\\frac{\\pi}{2}} \\frac{1}{f(x)}dx.$ Let's think step by step and put only the final answer within \... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 40050,
"solution": ""
} |
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