data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 2
values | reward_model dict | extra_info dict | metadata null |
|---|---|---|---|---|---|
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 5800,
"need_tools_kwargs": true,
"question": "In the Cartesian coordinate system $xOy$, given point $A(0,-2)$, point $B(1,-1)$, and $P$ is a moving point on the circle $x^{2}+y^{2}=2$, the maximum value of $\\dfrac {PB}{PA}$ is \\_\\_\\_\\_\\_\\_.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Kingston, Jamaica",
"style": "rule"
} | {
"index": 5801,
"need_tools_kwargs": true,
"question": "Where was the boxer that James Butler hit after a fight from?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Hubert Van Eyck",
"style": "rule"
} | {
"index": 5802,
"need_tools_kwargs": true,
"question": "Who is the sibling of the creator of The Portrait of a Man with a Blue Chaperon?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Fox8",
"style": "rule"
} | {
"index": 5803,
"need_tools_kwargs": true,
"question": "What channel broadcasted the competition that Van Den Dungen competed in at 16?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 5804,
"need_tools_kwargs": true,
"question": "给定整数 n\\geq3. 求最小的正整数 k，使得存在 k 元集合 A 和 n 个两两不同的实数 x_1,x_2,\\cdots,x_n，满足 x_1+x_2, x_2+x_3, \\cdots, x_{n-1}+x_n, x_n+x_1 都属于 A.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 5805,
"need_tools_kwargs": true,
"question": "Suppose that $X_1, X_2, \\ldots$ are real numbers between 0 and 1 that are chosen independently and uniformly at random. Let $S=\\sum_{i=1}^kX_i/2^i,$ where $k$ is the least positive integer such that $X_k<X_{k+1},$ or $k=\\infty$ if there is no such integer. Find the expected value of $S.$ The original answer is in the form $me^{n/m}-p$, please calculate the value of $m+n+p$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Den Nye Lensmannen",
"style": "rule"
} | {
"index": 5806,
"need_tools_kwargs": true,
"question": "Which film came out first, Den Nye Lensmannen or Tonio (Film)?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "79",
"style": "rule"
} | {
"index": 5807,
"need_tools_kwargs": true,
"question": "Each of five, standard, six-sided dice is rolled once. Two of the dice come up the same, but the other three are all different from those two and different from each other. The pair is set aside, and the other three dice are re-rolled. The dice are said to show a \"full house\" if three of the dice show the same value and the other two show the same value (and potentially, but not necessarily, all five dice show the same value). What is the probability that after the second set of rolls, the dice show a full house?The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "\\frac{3\\sqrt{2}}{\\sqrt{5}}",
"style": "rule"
} | {
"index": 5808,
"need_tools_kwargs": true,
"question": "If $4x^2+y^2=4$, what is the largest possible value of $|x|+|y|$?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"index": 5809,
"need_tools_kwargs": true,
"question": "Previously, on an old truck, I traveled from village $A$ through $B$ to village $C$. After five minutes, I asked the driver how far we were from $A$. \"Half as far as from $B,\" was the answer. Expressing my concerns about the slow speed of the truck, the driver assured me that while the truck cannot go faster, it maintains its current speed throughout the entire journey.\n\n$13$ km after $B$, I inquired again how far we were from $C$. I received exactly the same response as my initial inquiry. A quarter of an hour later, we arrived at our destination. How many kilometers is the journey from $A$ to $C$?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 5810,
"need_tools_kwargs": true,
"question": "一个\"面包圈\"是指从 (a+2)\\times(b+2) 矩形的中间去掉 a\\times b 矩形后得到的由 2a+2b+4 个单位方格构成的环，其中 a,b 是任意正整数.考虑无限大的方格表. 对每个偶数 n\\geq8，一个\"n-阶面包店\"是指由有限个方格构成的集合 S，满足对任意一个由 n 个方格构成的面包圈 B，存在与 B 全等（可平移和旋转）的面包圈，其方格都属于 S. 用 f(n) 表示 n-阶面包店中方格数的最小可能值.求实数 \\alpha，使得对任意充分大的偶数 n，均有\\df{1}{100}<\\df{f(n)}{n^\\alpha}<100.原始的答案是\\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "70",
"style": "rule"
} | {
"index": 5811,
"need_tools_kwargs": true,
"question": "All $20$ diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "no",
"style": "rule"
} | {
"index": 5812,
"need_tools_kwargs": true,
"question": "Do both directors of films Ramaiya Vastavaiya and Forbidden Temptations have the same nationality?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 5813,
"need_tools_kwargs": true,
"question": "Consider the sequence where each term is derived from the square of the units digit of each corresponding Fibonacci number. For example, if a Fibonacci number is 57, the corresponding term in this new sequence would be \\(7^2 = 49\\), and its units digit would be 9. Determine which digit from 0 to 9 is the last to appear in the units position of this new sequence.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 5814,
"need_tools_kwargs": true,
"question": "The captain's assistant, who had been overseeing the loading of the ship, was smoking one pipe after another from the very start of the process. When $2 / 3$ of the number of loaded containers became equal to $4 / 9$ of the number of unloaded containers, and noon struck, the old sea wolf started smoking his next pipe. When he finished this pipe, the ratio of the number of loaded containers to the number of unloaded containers reversed the ratio that existed before he began smoking this pipe. How many pipes did the second assistant smoke during the loading period (assuming the loading rate and the smoking rate remained constant throughout)?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Los Angeles",
"style": "rule"
} | {
"index": 5815,
"need_tools_kwargs": true,
"question": "Where was the place of death of Ben Gage's wife?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "20 November 2014",
"style": "rule"
} | {
"index": 5816,
"need_tools_kwargs": true,
"question": "What is the date of death of Eugenia Martínez De Irujo, 12Th Duchess Of Montoro's mother?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "125",
"style": "rule"
} | {
"index": 5817,
"need_tools_kwargs": true,
"question": "For any positive integer $a,$ $\\sigma(a)$ denotes the sum of the positive integer divisors of $a$ . Let $n$ be the least positive integer such that $\\sigma(a^n)-1$ is divisible by $2021$ for all positive integers $a$ . Find the sum of the prime factors in the prime factorization of $n$ .",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "\\log(3) + \\frac{8}{3}",
"style": "rule"
} | {
"index": 5818,
"need_tools_kwargs": true,
"question": "Compute the definite integral:\n\n$$\n\\int_{-5 / 3}^{1} \\frac{\\sqrt[3]{3x+5} + 2}{1 + \\sqrt[3]{3x+5}} \\, dx\n$$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "2007, 2738, 3122",
"style": "rule"
} | {
"index": 5819,
"need_tools_kwargs": true,
"question": "I ponder some numbers in bed, all products of three primes I've said, apply \\(\\phi\\) they're still fun:\n\\[ n = 37^{2} \\cdot 3 \\ldots \\]\n\\[ \\phi(n) = \\]\n\\[ 11^{3} + 1 ? \\]\nWhat numbers could be in my head?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "80\\%",
"style": "rule"
} | {
"index": 5820,
"need_tools_kwargs": true,
"question": "Laura took six trips to park. On each trip, she spent 2 hours at the park and an additinal 30 minutes walking to and from the park. What percentage of the total time she took for her trips to the park did Laura spend in the park?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"index": 5821,
"need_tools_kwargs": true,
"question": "Let \\(A = (-4,5,-17)\\) and \\(B = (34,15,5).\\) Let \\(P\\) be the set of points in space such that triangle \\(ABP\\) is equilateral. The set of points \\(P\\) in space that satisfy this condition traces a curve. The original answer is in the form of \\(k\\pi\\), please find the value of \\(k\\).",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 5822,
"need_tools_kwargs": true,
"question": "The number of positive integers \\( x \\) with \\( x \\leq 60 \\) such that each of the rational expressions\n\n\\[\n\\frac{7 x + 1}{2}, \\frac{7 x + 2}{3}, \\frac{7 x + 3}{4}, \\cdots, \\frac{7 x + 300}{301}\n\\]\n\nis in lowest terms (i.e., in each expression, the numerator and denominator have no common factors) is\n(A) 1\n(B) 2\n(C) 3\n(D) 4\n(E) 5",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 5823,
"need_tools_kwargs": true,
"question": "A clue \"$k$ digits, sum is $n$\" gives a number $k$ and the sum of $k$ distinct, nonzero digits. An answer for that clue consists of $k$ digits with sum $n$. For example, the clue \"Three digits, sum is 23\" has only one answer: $6,8,9$. The clue \"Three digits, sum is 8\" has two answers: $1,3,4$ and $1,2,5$.\nIf the clue \"Four digits, sum is $n$\" has the largest number of answers for any four-digit clue, then what is the value of $n$? How many answers does this clue have? Explain why no other four-digit clue can have more answers.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "King Willem-Alexander",
"style": "rule"
} | {
"index": 5824,
"need_tools_kwargs": true,
"question": "Who is Jorge Zorreguieta's daughter married to?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Tbilisi",
"style": "rule"
} | {
"index": 5825,
"need_tools_kwargs": true,
"question": "Where was the director of film Coordinates Of Death born?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Blind Chance",
"style": "rule"
} | {
"index": 5826,
"need_tools_kwargs": true,
"question": "Which film has the director who was born later, Doctor Praetorius (Film) or Blind Chance?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "1024",
"style": "rule"
} | {
"index": 5827,
"need_tools_kwargs": true,
"question": "Suppose that at some point Joe B. has placed 2 black knights on the original board, but gets bored of chess. He now decides to cover the 34 remaining squares with 17 dominos so that no two overlap and the dominos cover the entire rest of the board. For how many initial arrangements of the two pieces is this possible?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Transylvania",
"style": "rule"
} | {
"index": 5828,
"need_tools_kwargs": true,
"question": "Where was the father of Margaret Of Hungary (Saint) born?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "26 February 1632",
"style": "rule"
} | {
"index": 5829,
"need_tools_kwargs": true,
"question": "What is the date of death of Vespasiano Vincenzo Gonzaga's father?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 5830,
"need_tools_kwargs": true,
"question": "Giraldo wrote five distinct natural numbers on the vertices of a pentagon. Next, he wrote on each side of the pentagon the least common multiple (LCM) of the numbers written on the two vertices of that side. He noticed that the five numbers written on the sides were equal. What is the smallest number Giraldo could have written on the sides?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 5831,
"need_tools_kwargs": true,
"question": "A motorboat and a kayak both depart from point \\( A \\) on a river traveling downstream. The kayak moves at the speed of the river current plus an additional 2 km/h due to paddling effort. The motorboat travels at a constant speed with respect to the river. After reaching point \\( B \\) downstream, the motorboat immediately turns around and travels back upstream. It meets the kayak on the river 12 hours after both left point \\( A \\). Determine how many hours it took the motorboat to travel from \\( A \\) to \\( B \\).",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "October 23 to October 30",
"style": "rule"
} | {
"index": 5832,
"need_tools_kwargs": true,
"question": "What were the dates of the Pan American Games in which Roman Gastaldi competed two years prior to competing in the World Championships in Moscow?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "\\frac{5}{54}",
"style": "rule"
} | {
"index": 5833,
"need_tools_kwargs": true,
"question": "A cube with edge length of 3 inches is composed of 27 unit cubes. Among these, 21 are red and 6 are white. If you arrange the cubes such that the smallest possible area of the cube's surface is white, what fraction of the total surface area is white?\n(A) $\\frac{5}{54}$\n(B) $\\frac{1}{9}$\n(C) $\\frac{5}{27}$\n(D) $\\frac{2}{9}$\n(E) $\\frac{1}{3}$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Aqua",
"style": "rule"
} | {
"index": 5834,
"need_tools_kwargs": true,
"question": "What user interface used by Apple is compared to the RK Launcher?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Stromeferry railway station",
"style": "rule"
} | {
"index": 5835,
"need_tools_kwargs": true,
"question": "What railway station is around 3.5 miles south-west of the village of Lochcarron?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "June 16, 1979",
"style": "rule"
} | {
"index": 5836,
"need_tools_kwargs": true,
"question": "What is the date of death of the director of film Party Girl (1958 Film)?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "opera",
"style": "rule"
} | {
"index": 5837,
"need_tools_kwargs": true,
"question": "Háry János and Fedora, are which type of dramatic play?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "5 January 1066",
"style": "rule"
} | {
"index": 5838,
"need_tools_kwargs": true,
"question": "When did the king that Walter D'Aincourt was a landholder under die?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "\"King of Cool\"",
"style": "rule"
} | {
"index": 5839,
"need_tools_kwargs": true,
"question": "By what nickname was the star of Murderers' Row known? ",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "French",
"style": "rule"
} | {
"index": 5840,
"need_tools_kwargs": true,
"question": "What country of origin does Vichy France and Philippe Pétain have in common?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 5841,
"need_tools_kwargs": true,
"question": "An ellipse with its focus on the $x$-axis has the equation $\\frac{x^2}{4} + \\frac{y^2}{b^2} = 1$ and an eccentricity of $e = \\frac{1}{2}$. Let $F$ and $A$ be the left focus and right vertex of the ellipse, respectively, and let $P$ be any point on the ellipse. Determine the maximum value of $\\overrightarrow{PF} \\cdot \\overrightarrow{PA}$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "462",
"style": "rule"
} | {
"index": 5842,
"need_tools_kwargs": true,
"question": "Katka cut out 20 rectangles from paper. The first had dimensions $1 \\mathrm{~cm} \\times 2 \\mathrm{~cm}$, the second $2 \\mathrm{~cm} \\times 3 \\mathrm{~cm}$, the third $3 \\mathrm{~cm} \\times 4 \\mathrm{~cm}$, and so on. She then started arranging them by connecting sides of the same length so that they do not overlap and no rectangle touches more than two other rectangles.\n\na) Draw the polygon that Katka formed from the first six of her rectangles.\n\nb) Determine the perimeter of the polygon formed by all the rectangles Katka cut out.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "New York City",
"style": "rule"
} | {
"index": 5843,
"need_tools_kwargs": true,
"question": "Slim till Dead is a 2005 Hong Kong film starring a Taiwan-born Hong Kong actress who moved to what city at a young age?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Los Angeles",
"style": "rule"
} | {
"index": 5844,
"need_tools_kwargs": true,
"question": "Where did the director of film Tarzan And The Jungle Boy die?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "American",
"style": "rule"
} | {
"index": 5845,
"need_tools_kwargs": true,
"question": "What nationality is the director of film A Perfect Couple?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "100\\sqrt{3}",
"style": "rule"
} | {
"index": 5846,
"need_tools_kwargs": true,
"question": "The side length of the regular hexagon is 10 cm. What is the number of square centimeters in the area of the shaded region? Express your answer in simplest radical form.\n\n[asy]\nsize(100);\n\npair A,B,C,D,E,F;\nA = dir(0); B = dir(60); C = dir(120); D = dir(180); E = dir(240); F = dir(300);\n\nfill(B--C--E--F--cycle,heavycyan);\n\ndraw(A--B--C--D--E--F--A);\n[/asy]",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "December 6, 1899",
"style": "rule"
} | {
"index": 5847,
"need_tools_kwargs": true,
"question": "When is the director of film Billy The Kid Trapped 's birthday?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "131",
"style": "rule"
} | {
"index": 5848,
"need_tools_kwargs": true,
"question": "Luis wrote the sequence of natural numbers starting from 1:\n\n$$\n1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, \\cdots\n$$\n\nWhen did he write the digit 3 for the 25th time?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "30\\%",
"style": "rule"
} | {
"index": 5849,
"need_tools_kwargs": true,
"question": "In a stockpile of products produced by 3 machines m1, m2, and m3, 40% were manufactured by m1 and a certain percentage were manufactured by m2. 3% of the products of m1 are defective, 1% of products of m2 are defective, while 93% of the products of m3 are not defective. The percentage of defective products in the stockpile is 3.6%. What is the percentage of products manufactured by m2?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"index": 5850,
"need_tools_kwargs": true,
"question": "Let $\\triangle ABC$ be a right-angled triangle in the $xy$ plane, with $C$ as the right angle. The hypotenuse $AB$ has a length of 60. The medians drawn from points $A$ and $B$ lie on the lines $y = x + 3$ and $y = 2x + 4$, respectively. Find the area of $\\triangle ABC$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 5851,
"need_tools_kwargs": true,
"question": "For certain natural numbers $n$, the numbers $2^{n}$ and $5^{n}$ share the same leading digit. What are these possible leading digits?\n\n(The 14th All-Russian Mathematical Olympiad, 1988)",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 5852,
"need_tools_kwargs": true,
"question": "Using the four digits 1, 9, 8, and 5, form a number in the structure \\(a^{b^{c^{d}}}\\) to maximize its value. What value should be assigned to \\(c\\) in order to achieve this maximum?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "over 300 retailers",
"style": "rule"
} | {
"index": 5853,
"need_tools_kwargs": true,
"question": "How many retailers are there in the Souk across from The Dubai Textile Souk?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 5854,
"need_tools_kwargs": true,
"question": "Bob grew corn in his garden this year and ended up with 50 bushels. He gave away corn to his friends, and after giving away corn, Bob has 357 ears of corn left. If each bushel contained 14 ears of corn, how many bushels did Bob give to his friend Terry?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Sam Duckworth",
"style": "rule"
} | {
"index": 5855,
"need_tools_kwargs": true,
"question": "Which English musician's stage name came from a British magazine?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 5856,
"need_tools_kwargs": true,
"question": "设 x_1,x_2,x_3,x_4 均是正整数，且 \\{x_ix_jx_k\\ |\\ 1\\leq i<j<k\\leq 4\\}=\\{18,36,54\\}. 则 x_1+x_2+x_3+x_4=__________.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"index": 5857,
"need_tools_kwargs": true,
"question": "The cube root of the real number $-27$ is ____.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "no",
"style": "rule"
} | {
"index": 5858,
"need_tools_kwargs": true,
"question": "Do both directors of films Jean De Florette and Eedu Gold Ehe have the same nationality?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Western Division",
"style": "rule"
} | {
"index": 5859,
"need_tools_kwargs": true,
"question": "With which division of the Southeastern Conference the football program compete in which Damontre Lamounte Moore played college football and earned All-American honors? ",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "(-2,1)",
"style": "rule"
} | {
"index": 5860,
"need_tools_kwargs": true,
"question": "Given that the solution set of the quadratic inequality $ax^{2}+bx+c < 0$ with respect to $x$ is $(-\\infty,-1)\\cup( \\frac {1}{2},+\\infty)$, determine the solution set of the inequality $cx^{2}-bx+a < 0$.\nA: $(-1,2)$\nB: $(-\\infty,-1)\\cup(2,+\\infty)$\nC: $(-2,1)$\nD: $(-\\infty,-2)\\cup(1,+\\infty)$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 5861,
"need_tools_kwargs": true,
"question": "Find all real numbers $x, y, z$ so that\n\\begin{align*}\n x^2 y + y^2 z + z^2 &= 0 \\\\\n z^3 + z^2 y + z y^3 + x^2 y &= \\frac{1}{4}(x^4 + y^4).\n\\end{align*}\nThe original answer is in the form mx = ny = pz = q. Please find the value of m + n + p + q.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "1,904,806 people",
"style": "rule"
} | {
"index": 5862,
"need_tools_kwargs": true,
"question": "A1 road continues to be N1 road and M1 motorway at a city that had how many inhabitants in 2016 ?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "yes",
"style": "rule"
} | {
"index": 5863,
"need_tools_kwargs": true,
"question": "Are Aminabad, Firuzkuh and Shah Pahneh both located in the same country?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "986",
"style": "rule"
} | {
"index": 5864,
"need_tools_kwargs": true,
"question": "Given that \\(X\\), \\(Y\\), and \\(Z\\) are different digits, determine the largest possible three-digit sum for the expression represented by the following arrangement:\n\n\\[\n\\begin{array}{ccc}\nX & X & X \\\\\n& Y & X \\\\\n+ & & X \\\\\n\\hline\n\\end{array}\n\\]\n\nExpress your answer in the form of a three-digit number and explain your reasoning.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 5865,
"need_tools_kwargs": true,
"question": "设整数 n\\geq2. 某天 n 个人组成了一个社团，每人向政府交 1 元注册费。接下来每天都发生如下事情：每一个前一天组建的社团都分裂成两个团体，其中含至少两人的团体组建成一个新社团，每个新社团的成员向政府交 1 元注册费，只有一名成员的团体不再组建新社团。上述过程直到不能继续进行下去为止。求政府总共收到的注册费的最大值和最小值。最大值的答案形如\\frac{k}{2}n(n+1) + m，最小值的答案形如(\\lceil\\log_2n\\rceil+p)n-q^{\\lceil\\log_2n\\rceil}，请给出k+m+p+q的值。",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "about 20 years",
"style": "rule"
} | {
"index": 5866,
"need_tools_kwargs": true,
"question": "How long did the bombing of a Toronto–Montreal–London–Delhi route of Air India have an effect on Canada-India relations for?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "no",
"style": "rule"
} | {
"index": 5867,
"need_tools_kwargs": true,
"question": "Do the movies Coolin' (Music Video) and Friend Zone (Film), originate from the same country?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "1986",
"style": "rule"
} | {
"index": 5868,
"need_tools_kwargs": true,
"question": "In what year was the actress who was starred in \"Streak\" with Rumer Willis born?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "August 17, 2017",
"style": "rule"
} | {
"index": 5869,
"need_tools_kwargs": true,
"question": "When was the friends song was released which is taken from the fourth studio album of canadian singer and song writer Justin Bieber?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Salinas, California",
"style": "rule"
} | {
"index": 5870,
"need_tools_kwargs": true,
"question": "In what city and state was the Chief of Mental Health (1959-1979) of the integrated managed care consortium based in Oakland, California, United Stated founded in 1945 by industrialist Henry J. Kaiser and physician Sidney Garfield, born?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"index": 5871,
"need_tools_kwargs": true,
"question": "In a geometric sequence $\\{a_n\\}$ where each term is positive, $a_1=2$, and $2a_1$, $a_3$, $3a_2$ form an arithmetic sequence. \n(Ⅰ) Find the general formula for the geometric sequence $\\{a_n\\}$. \n(Ⅱ) If the sequence $\\{b_n\\}$ satisfies $b_n=11-2\\log_2a_n$, find the maximum value of the sum of the first $n$ terms of $\\{b_n\\}$, denoted as $T_n$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 5872,
"need_tools_kwargs": true,
"question": "已知 $y, f, d$ 为正整数, $f(x)=(1+x)^{y}+(1+x)^{f}+(1+x)^{d}$. 其中 $x$ 的系数为 10, 则 $x^{2}$ 的系数的最大可能值与最小可能值之和为 $\\qquad$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "\\sqrt{30}",
"style": "rule"
} | {
"index": 5873,
"need_tools_kwargs": true,
"question": "Given the curve defined by the parametric equations $\\begin{cases} x=2-t\\sin 30^\\circ \\\\ y=-1+t\\sin 30^\\circ \\end{cases}$ (with $t$ as the parameter) intersects with the curve $x^2+y^2=8$ at points $B$ and $C$, find the value of $|BC|$.\n\nA: $2\\sqrt{7}$\n\nB: $\\sqrt{60}$\n\nC: $7\\sqrt{2}$\n\nD: $\\sqrt{30}$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 5874,
"need_tools_kwargs": true,
"question": "设 a, b, c 是乘积为 1 的复数，a, b, c 都不是实数且模长都不是 1。记p=(a+b+c)+\\left(\\dfrac{1}{a}+\\dfrac{1}{b}+\\dfrac{1}{c}\\right),\\quad q=\\dfrac{a}{b}+\\dfrac{b}{c}+\\dfrac{c}{a}。已知 p, q 都是实数，求所有可能的数对 (x, y) 形式的 (p, q)，并给出 x + y 的值。",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Richard Nixon",
"style": "rule"
} | {
"index": 5875,
"need_tools_kwargs": true,
"question": "What president did the chairman of the Commission on Protecting and Reducing Government Secrecy serve as an advisor to?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "\\frac{21}{10}",
"style": "rule"
} | {
"index": 5876,
"need_tools_kwargs": true,
"question": "In a rectangular prism \\( ABCD-A_1B_1C_1D_1 \\), where \\( AB = 5 \\), \\( AD = 3 \\), and \\( AA_1 = 4 \\), a plane \\(\\alpha\\) passing through point \\( A \\) and parallel to line \\( CD \\) divides the prism into two parts. Now, two spheres are placed inside these two parts of the prism. As the plane \\(\\alpha\\) changes, what is the maximum value of the sum of the radii of these two spheres?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 5877,
"need_tools_kwargs": true,
"question": "A positive integer $n$ is considered lucky if the numbers $2n + 1$, $3n + 1$, and $4n + 1$ are all composite. Determine the smallest lucky number.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 5878,
"need_tools_kwargs": true,
"question": "若实数 $x, y$ 满足 $4 x^{2}-4 x y+2 y^{2}=1$ ，则 $3 x^{2}+x y+y^{2}$ 的最大值与最小值的和为 $\\qquad$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "223",
"style": "rule"
} | {
"index": 5879,
"need_tools_kwargs": true,
"question": "There are ten weights of different weights, each weighing an integer number of grams. It is known that the weight of the lightest weight and the heaviest weight differ by 9 grams. One weight is lost. Determine its weight if the total weight of the remaining weights is 2022 grams.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Pink rhododendron",
"style": "rule"
} | {
"index": 5880,
"need_tools_kwargs": true,
"question": "which is the state flower of himachal pradesh",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Nicholas Pirotton",
"style": "rule"
} | {
"index": 5881,
"need_tools_kwargs": true,
"question": "What was the name of the sculptor who created the war memorial, a twenty-two-and-a-half-foot statue of bronze and granite depicting a Canadian soldier in battle dress, in Brockville, Ontario, that was unveiled in 1924?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "sister company",
"style": "rule"
} | {
"index": 5882,
"need_tools_kwargs": true,
"question": "Kalitta Charters is what to Kalitta Air ?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Tromsø",
"style": "rule"
} | {
"index": 5883,
"need_tools_kwargs": true,
"question": "Which town, with a population of 64,376 is bordered by Jiehkkevárri?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "(-3, 4)",
"style": "rule"
} | {
"index": 5884,
"need_tools_kwargs": true,
"question": "The vertices of a rectangle have coordinates \\((1,3)\\), \\((1,1)\\), \\((4,1)\\), and \\((4,3)\\). If the rectangle is reflected in the \\(y\\)-axis, which of the following points is not a vertex of the reflected rectangle?\n(A) \\((-1,1)\\)\n(B) \\((-4,1)\\)\n(C) \\((-3,4)\\)\n(D) \\((-1,3)\\)\n(E) \\((-4,3)\\)",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 5885,
"need_tools_kwargs": true,
"question": "In a class, $36$ students participate in extracurricular research groups for mathematics, physics, and chemistry. Each student can participate in at most two groups. It is known that the numbers of students participating in the mathematics, physics, and chemistry groups are $26$, $15$, and $13$ respectively. There are $6$ students who participate in both mathematics and physics groups, and $4$ students who participate in both physics and chemistry groups. Find the number of students who participate in both mathematics and chemistry groups.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "4:13",
"style": "rule"
} | {
"index": 5886,
"need_tools_kwargs": true,
"question": "the circulation for magazine p in 1971 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1972 - 1980 . what is the ratio of the circulation in 1971 to the total circulation during 1971 - 1980 for magazine p ?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "Riverina",
"style": "rule"
} | {
"index": 5887,
"need_tools_kwargs": true,
"question": "In what region of New South Wales, Australia was Dame Ella Macknight born? ",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "High Sheriff of Lancashire",
"style": "rule"
} | {
"index": 5888,
"need_tools_kwargs": true,
"question": "What ancient officer in North West England is the second Baronet of the Heywood baronets?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 5889,
"need_tools_kwargs": true,
"question": "已知数列 $\\left\\{a_{n}\\right\\}$ 满足:\n$a_{1}=a_{2}=1$ ，\n$a_{n+1}=\\frac{n^{2} a_{n}^{2}+5}{\\left(n^{2}-1\\right) a_{n-1}}(n>1)$.\n问：是否存在实数 $x 、 y(x \\neq 0)$ ，使得 $\\left\\{\\frac{b_{n+2}+b_{n}}{b_{n+1}}\\right\\}$ (其中, $b_{n}=(n x+y) a_{n}, n \\in \\mathbf{Z}_{+}$)为常值数列? 如果存在，请将$x$和$y$表示为m和n，并求出m+n的值。",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "17.22",
"style": "rule"
} | {
"index": 5890,
"need_tools_kwargs": true,
"question": "Triangle $ABC$ has sides $AB = 31$, $AC = 29$, and $BC = 30$. Point $I$ is the intersection of the angle bisectors within triangle $ABC$. Find the length of $BI$.\nA. $20$\nB. $17.22$\nC. $18.54$\nD. $15$\nE. $16.82$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 5891,
"need_tools_kwargs": true,
"question": "In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , $X$ in centimeters?\n\n$\\textbf{(A)}\\hspace{.05in}1\\qquad\\textbf{(B)}\\hspace{.05in}2\\qquad\\textbf{(C)}\\hspace{.05in}3\\qquad\\textbf{(D)}\\hspace{.05in}4\\qquad\\textbf{(E)}\\hspace{.05in}5$",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "158°",
"style": "rule"
} | {
"index": 5892,
"need_tools_kwargs": true,
"question": "The smallest positive angle that has the same terminal side as -2002° is.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "American",
"style": "rule"
} | {
"index": 5893,
"need_tools_kwargs": true,
"question": "Which country the performer of song Animal Crackers In My Soup is from?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "652400",
"style": "rule"
} | {
"index": 5894,
"need_tools_kwargs": true,
"question": "Let $x, y, z$ be positive real numbers such that $x + y + z = 1399$. Find the maximum value of $\\lfloor x \\rfloor y + \\lfloor y \\rfloor z + \\lfloor z \\rfloor x$, where $\\lfloor a \\rfloor$ is the greatest integer not exceeding $a$.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"index": 5895,
"need_tools_kwargs": true,
"question": "Given an integer \\( n > 1 \\) and a \\( n \\times n \\) grid \\( ABCD \\) containing \\( n^2 \\) unit squares, each unit square is colored by one of three colors: Black, white, and gray. A coloring is called *symmetry* if each unit square with its center on diagonal \\( AC \\) is colored gray, and every pair of unit squares that are symmetric about \\( AC \\) must be colored either both black or both white. In each gray square, the label is \\( 0 \\); in a white square, a positive integer is labeled; and in a black square, a negative integer is labeled. A label is called \\( k \\)-*balance* (with \\( k \\in \\mathbb{Z}^+ \\)) if it satisfies the following requirements:\n\n1. Each pair of unit squares that are symmetric about \\( AC \\) are labeled with the same integer from the closed interval \\([-k, k]\\).\n2. If a row and a column intersect at a square colored black, then the set of positive integers in that row and the set of positive integers in that column must be distinct. If they intersect at a square colored white, then the set of negative integers in that row and the set of negative integers in that column must be distinct.\n\nFor \\( n = 5 \\), determine the minimum value of \\( k \\) such that there exists a \\( k \\)-balance label for the specified grid.\n\nAdditionally, for \\( n = 2017 \\), find the least value of \\( k \\) such that there is always a \\( k \\)-balance label for a symmetry coloring.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "252",
"style": "rule"
} | {
"index": 5896,
"need_tools_kwargs": true,
"question": "Xiaofang calculates the least common multiple (LCM) of two two-digit numbers represented as $\\overline{AB}$ and $\\overline{CD}$. Xiaoyuan calculates the LCM of two two-digit numbers represented as $\\overline{BA}$ and $\\overline{DC}$. It is known that the result Xiaofang gets is 1.75 times that of Xiaoyuan. Determine the LCM that Xiaofang calculates.",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 5897,
"need_tools_kwargs": true,
"question": "$\\triangle A B C$ 的三个顶点分别对应复数 $z_{1}, z_{2}, z_{3}$, 已知 $\\frac{z_{2}-z_{1}}{z_{3}-z_{1}}=1+2 \\mathrm{i}$。求 $\\triangle A B C$ 的面积与其最长边的长的平方的比。答案的形式为\\(\\frac{k}{m}\\)，请给出k+m的值。",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "progressive metal",
"style": "rule"
} | {
"index": 5898,
"need_tools_kwargs": true,
"question": "What type of music did the band play that was both founded in 1994, and had an album released in 1994 and reissued in 2000 through InsideOut Music?",
"split": "train"
} | null |
DR_grpo_mix | [
{
"content": "You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wiki... | qa | {
"ground_truth": "American",
"style": "rule"
} | {
"index": 5899,
"need_tools_kwargs": true,
"question": "What nationality is the director of film The Reckless Lady?",
"split": "train"
} | null |
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