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": "120^\\circ",
"style": "rule"
} | {
"index": 2000,
"need_tools_kwargs": true,
"question": "Circle $\\Gamma$ is the incircle of $\\triangle ABC$ and is also the circumcircle of $\\triangle XYZ$. The point $X$ is on $\\overline{BC}$, point $Y$ is on $\\overline{AB}$, and the point $Z$ is on $\\overline{AC}$. If $\\angle A=40^\\circ$, $\\angle B=60^\\circ$, and $\\angle C=80^\\circ$, what is the measure of $\\angle AYX$?",
"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": 2001,
"need_tools_kwargs": true,
"question": "Do director of film I Never Been In Vienna and director of film Menno'S Mind 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": "x + y - 1 = 0",
"style": "rule"
} | {
"index": 2002,
"need_tools_kwargs": true,
"question": "If the midpoint of a chord AB of the circle $x^2+y^2+2x-4y+m=0$ (where $m<3$) is $P(0,1)$, then the equation of the line containing the diameter perpendicular to AB 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... | math | {
"ground_truth": "A: \\frac{\\sqrt{5}}{5}",
"style": "rule"
} | {
"index": 2003,
"need_tools_kwargs": true,
"question": "Given that the vector $\\overrightarrow{n} = (2, 0, 1)$ is a normal vector of the plane $\\alpha$, and point $A(-1, 2, 1)$ lies on $\\alpha$, find the distance from point $P(1, 2, -2)$ to the plane $\\alpha$.\nOptions:\nA: $\\frac{\\sqrt{5}}{5}$\nB: $\\sqrt{5}$\nC: $2\\sqrt{5}$\nD: $\\frac{\\sqrt{5}}{10}$",
"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": "a metaphor and allusion",
"style": "rule"
} | {
"index": 2004,
"need_tools_kwargs": true,
"question": "\"Teletubbies say \"Eh-oh!\" is a single which contains a nursery rhyme that has been used in literature and popular culture as what?",
"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": "Central and Eastern Europe",
"style": "rule"
} | {
"index": 2005,
"need_tools_kwargs": true,
"question": "Kettenbrücke-Walzer commemorated the construction of the first chain bridge over a river located in which part of Europe ?",
"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": "2821",
"style": "rule"
} | {
"index": 2006,
"need_tools_kwargs": true,
"question": "The king said to the queen:\n\n- Now I am twice as old as you were when I was as old as you are now. When you are as old as I am now, our combined ages will be 63 years.\n\nHow old are each of them?",
"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": "Settle",
"style": "rule"
} | {
"index": 2007,
"need_tools_kwargs": true,
"question": "Where was the father of Benjamin Franklin Bache (Journalist) 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": "[3, 5, 7, 9, 11, 13]",
"style": "rule"
} | {
"index": 2008,
"need_tools_kwargs": true,
"question": "By writing 6 different numbers, none of which is the number 1, in ascending order and multiplying them, Olya obtained the result 135135. Write down the numbers that Olya multiplied.",
"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": 2009,
"need_tools_kwargs": true,
"question": "What nationality is the performer of song Long Black Veil?",
"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": "Andrei Stanislavovich Olhovskiy",
"style": "rule"
} | {
"index": 2010,
"need_tools_kwargs": true,
"question": "Between Andrei Olhovskiy and Jelena Janković, who became a pro earlier?",
"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": "Hugh Anthony Quarshie",
"style": "rule"
} | {
"index": 2011,
"need_tools_kwargs": true,
"question": "What is the name of Ghanaian-born British actor, who has appears in the film \"Highlander\", and also appears in the 38th episode of 'Holby City' as consultant Ric Griffin?",
"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": "12",
"style": "rule"
} | {
"index": 2012,
"need_tools_kwargs": true,
"question": "对于整数 n \\geq 4，求最小的整数 f(n)，使得对于任意正整数 m，在集合 \\{m, m+1, \\cdots, m+n-1\\} 的任一 f(n) 元子集中，都有三个数两两互质。原始答案的形式为 \\left[\\frac{n+1}{k}\\right] + \\left[\\frac{n+1}{m}\\right] - \\left[\\frac{n+1}{n}\\right] + p，其中 k, m, n, p 是整数。请计算 k + m + n + p 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": "35.625",
"style": "rule"
} | {
"index": 2013,
"need_tools_kwargs": true,
"question": "Given three pairwise disjoint sets of people, \\( A, B, \\) and \\( C \\), the average ages of the people in these sets are as follows: the average age in set \\( A \\) is 30, in set \\( B \\) is 25, and in set \\( C \\) is 50. Additionally, the average ages for the unions of these sets are: \\( A \\cup B \\) is 27, \\( A \\cup C \\) is 42, and \\( B \\cup C \\) is 35. Determine the average age of the people in the combined set \\( A \\cup B \\cup 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... | qa | {
"ground_truth": "yes",
"style": "rule"
} | {
"index": 2014,
"need_tools_kwargs": true,
"question": "Are both Zareh Shuran and Varkan 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": "29",
"style": "rule"
} | {
"index": 2015,
"need_tools_kwargs": true,
"question": "At the beginning of the year, the price of a commodity was $200. During January, the price increased by $30\\%$. In February, the price then decreased by $10\\%$. During March, the price increased again by $20\\%$. Finally, in April, the price decreased by $x\\%$. If the price at the end of April was the same as it was at the beginning of the year, determine the percentage decrease $x$ for April.",
"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": "William H. Bonney",
"style": "rule"
} | {
"index": 2016,
"need_tools_kwargs": true,
"question": "The Return of the Living Dead starred the actor and director who played what role on The Tall Man?",
"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{68}{81}",
"style": "rule"
} | {
"index": 2017,
"need_tools_kwargs": true,
"question": "Given that $x = \\frac{3}{4}$ is a solution to the equation $108x^2 + 61 = 145x - 7,$ what is the other value of $x$ that solves the equation? Express your answer as a common fraction.",
"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": "4 September 1771",
"style": "rule"
} | {
"index": 2018,
"need_tools_kwargs": true,
"question": "What is the date of death of Henry Harford'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": "4",
"style": "rule"
} | {
"index": 2019,
"need_tools_kwargs": true,
"question": "Given a sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first $n$ terms $S_{n}$ related to $a_{n}$ by the equation $S_{n}=-b a_{n}+1-\\frac{1}{(1+b)^{n}}$, where $b$ is a constant independent of $n$ and $b \\neq -1$:\n\n(1) Find the expression for $a_{n}$ in terms of $b$ and $n$.\n\n(2) When $b=3$, from which term does the sequence $\\left\\{a_{n}\\right\\}$ satisfy $S_{n}-a_{n}>\\frac{1}{2}$?",
"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": 2020,
"need_tools_kwargs": true,
"question": "A group of friends decided to play a computer game. Any two people either play together or against each other. Moreover, if player \\(A\\) plays together with \\(B\\), and \\(B\\) plays against \\(C\\), then \\(A\\) also plays against \\(C\\). How many friends are in the group if each player had exactly 15 opponents? List all possible options.",
"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": "\\$160",
"style": "rule"
} | {
"index": 2021,
"need_tools_kwargs": true,
"question": "If Patty's dress was $10 more than Ida's dress, and Ida's dress was $30 more than Jean's dress, and Jean's dress was $10 less than Pauline's dress, and lastly Pauline's dress was $30, how much did all the ladies spend on dresses put together?",
"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": "heart attack",
"style": "rule"
} | {
"index": 2022,
"need_tools_kwargs": true,
"question": "Why did the director of film The Silent Avenger 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... | math | {
"ground_truth": "83",
"style": "rule"
} | {
"index": 2023,
"need_tools_kwargs": true,
"question": "Square \\(ABCD\\) has side length \\(4\\). Points \\(P\\) and \\(Q\\) are located on sides \\(BC\\) and \\(CD\\), respectively, such that \\(BP = DQ = 1\\). Let \\(AQ\\) intersect \\(DP\\) at point \\(X\\). Compute the area of triangle \\(PQX\\). The original answer is in \\(\\frac{k}{m}\\) format, please give the value of \\(k + m\\).",
"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": "Philadelphia",
"style": "rule"
} | {
"index": 2024,
"need_tools_kwargs": true,
"question": "The author of the book Ticket to Ride spent 36 years as a news anchor in which city ?",
"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": "Castellina in Chianti",
"style": "rule"
} | {
"index": 2025,
"need_tools_kwargs": true,
"question": "Where did the director of film A Glass Of Water (1960 Film) 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... | math | {
"ground_truth": "132",
"style": "rule"
} | {
"index": 2026,
"need_tools_kwargs": true,
"question": "Let $g$ be a function from the nonnegative integers to the nonnegative integers, such that\n\\[ 2g(a^2 + 2b^2) = [g(a)]^2 + 2[g(b)]^2 \\]\nfor all nonnegative integers $a$ and $b$.\n\nLet $m$ be the number of possible values of $g(13)$, and let $t$ be the sum of the possible values of $g(13)$. Find $m \\times t$.",
"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": 2027,
"need_tools_kwargs": true,
"question": "Did Pamela Wible and Gardner Budd share 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": "1020",
"style": "rule"
} | {
"index": 2028,
"need_tools_kwargs": true,
"question": "When a positive integer $N$ is fed into a machine, the output is calculated according to the rule below. For example, if the input is $N=8$, the output is $4 \\cdot 8 + 2 = 34$. When this output is repeatedly inserted into the machine seven more times, the final output is $50$.\n\\[8 \\to 34 \\to 17 \\to 70 \\to 35 \\to 142 \\to 71 \\to 286 \\to 50\\]\nFind the sum of all such integers $N$ where, after applying the same 8-step process, the final output is $2$.\n\\[N \\to \\cdots \\to 2\\]\nA) 930\nB) 960\nC) 980\nD) 1000\nE) 1020",
"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": "Cevat, Avni and Faruk Yerli",
"style": "rule"
} | {
"index": 2029,
"need_tools_kwargs": true,
"question": "Who founded the company that created the game engine used to make Far Cry?",
"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": 2030,
"need_tools_kwargs": true,
"question": "Do both films: Umrao Jaan (1981 Film) and Big Tremaine have the directors 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": "yes",
"style": "rule"
} | {
"index": 2031,
"need_tools_kwargs": true,
"question": "Are Valian, Alborz and Pa Baz 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... | qa | {
"ground_truth": "1,100 students",
"style": "rule"
} | {
"index": 2032,
"need_tools_kwargs": true,
"question": "How many students are presently enrolled at the high school fed by the city in northeast Oakland County, Michigan?",
"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 \\sqrt{3} - 16",
"style": "rule"
} | {
"index": 2033,
"need_tools_kwargs": true,
"question": "Let $x$ and $y$ be positive real numbers such that\n\\[\\frac{1}{x + 3} + \\frac{2}{y + 3} = \\frac{1}{4}.\\] Find the minimum value of $2x + 3y.$",
"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": "NWP",
"style": "rule"
} | {
"index": 2034,
"need_tools_kwargs": true,
"question": "What is the abbreviation of the passage discovered by Hudson and Button?",
"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": 2035,
"need_tools_kwargs": true,
"question": "A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball?",
"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": "Tom Felton",
"style": "rule"
} | {
"index": 2036,
"need_tools_kwargs": true,
"question": "Who had a role acting in Trojan Bellisario and Harry Potter?",
"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{14}{3}",
"style": "rule"
} | {
"index": 2037,
"need_tools_kwargs": true,
"question": "Suppose a die is rolled. There are two opportunities to roll: you can choose to roll just once, or twice, but the result is determined by the last roll. What is the expected value of the outcome in this scenario? If there are three opportunities, still taking the value of the last roll, what is the expected value of the outcome?",
"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": 2038,
"need_tools_kwargs": true,
"question": "Do director of film Pellaindi Kaani and director of film Chilly Scenes Of Winter (Film) 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": "|\\overrightarrow {u}| = \\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"index": 2039,
"need_tools_kwargs": true,
"question": "Let vector $\\overrightarrow {a} = (\\cos 23°,\\cos 67°)$ and vector $\\overrightarrow {b} = (\\cos 68°,\\cos 22°)$. \n(1) Find the dot product $\\overrightarrow {a} \\cdot \\overrightarrow {b}$. \n(2) If vector $\\overrightarrow {b}$ is collinear with vector $\\overrightarrow {m}$ and $\\overrightarrow {u} = \\overrightarrow {a} + \\overrightarrow {m}$, find the minimum value of the magnitude of vector $\\overrightarrow {u}$.",
"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": "\"the military capital of the American Revolution\"",
"style": "rule"
} | {
"index": 2040,
"need_tools_kwargs": true,
"question": "What term has been applied to the town where Louis Alan Hazeltine was 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": "15",
"style": "rule"
} | {
"index": 2041,
"need_tools_kwargs": true,
"question": "A two-digit integer is divided by the sum of its digits. Find the largest remainder that can occur.",
"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": "24 November 1967",
"style": "rule"
} | {
"index": 2042,
"need_tools_kwargs": true,
"question": "When did the director of film The Mystery Of A Hansom Cab (1925 Film) 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": "Swift and Liz Rose",
"style": "rule"
} | {
"index": 2043,
"need_tools_kwargs": true,
"question": "\"Sparks Fly\" is a song written and recorded by American singer-songwriter Taylor Swift for her third studio album \"Speak Now\" (2010), Swift wrote the song when she was 16 years old, prior to the release of her debut single, in Tim McGraw, and first published song recorded by American singer-songwriter Taylor Swift, the song was written by which two people?",
"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": 2044,
"need_tools_kwargs": true,
"question": "Do both Bachke Rehna Re Baba and Blood Feud (1978 Film) films have the directors 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": "Ron Howard",
"style": "rule"
} | {
"index": 2045,
"need_tools_kwargs": true,
"question": " William Preston played a blacksmith in an American epic romantic adventure drama film directed by who? ",
"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{182}{243}",
"style": "rule"
} | {
"index": 2046,
"need_tools_kwargs": true,
"question": "Larry and Julius play a game where they each take turns throwing balls at a bottle, with Larry throwing first. They are allowed a total of 6 throws combined. The probability that Larry knocks off the bottle with each throw is \\(\\frac{2}{3}\\), while for Julius, it is \\(\\frac{1}{3}\\). Calculate the probability that Larry wins the game.",
"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": "7.2",
"style": "rule"
} | {
"index": 2047,
"need_tools_kwargs": true,
"question": "In triangle \\( \\triangle ABC \\), the area is \\( 18 \\). Points \\( D \\), \\( E \\), and \\( F \\) are located on sides \\( AB \\), \\( BC \\), and \\( CA \\) respectively, with \\( AD = 1 \\) and \\( DB = 4 \\). Given that triangles \\( \\triangle ABE \\) and quadrilateral \\( DBEF \\) have equal areas and segment \\( EF \\) equals the segment \\( AD \\), determine the area of triangle \\( \\triangle ABE \\).",
"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": "Czechoslovakia",
"style": "rule"
} | {
"index": 2048,
"need_tools_kwargs": true,
"question": "Anna-Lena Grönefeld is from Germany, whereas Pavel Složil is from where?",
"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^{1987} ",
"style": "rule"
} | {
"index": 2049,
"need_tools_kwargs": true,
"question": "Find the smallest positive integer $n$ such that \\[2^{1989}\\; \\vert \\; m^{n}-1\\] for all odd positive integers $m>1$ .",
"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": 2050,
"need_tools_kwargs": true,
"question": "Are Prospidnick and Shahrak-E Nur Mohammadi 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... | qa | {
"ground_truth": "Homestead",
"style": "rule"
} | {
"index": 2051,
"need_tools_kwargs": true,
"question": "Life Screams is an album by the singer from what Florida city?",
"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": "50",
"style": "rule"
} | {
"index": 2052,
"need_tools_kwargs": true,
"question": "Let $g(x)$ be a function defined on the domain $\\{x_a, x_b, x_c\\}$ such that the graph of $y = g(x)$ consists of exactly three points. These points construct a triangle with an area of 50 square units. Determine the area of the triangle formed by the points on the graph of the function $y = 3g(3x)$.",
"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": 2053,
"need_tools_kwargs": true,
"question": "What nationality is the director of film Gale Force?",
"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": 2054,
"need_tools_kwargs": true,
"question": "Sammy can eat 15 pickle slices. His twin sister Tammy can eat twice as much as Sammy. Their older brother Ron eats a certain percentage fewer pickle slices than Tammy. Ron eats 24 pickle slices. What is the percentage of pickle slices Ron eats less than Tammy?",
"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": "BD",
"style": "rule"
} | {
"index": 2055,
"need_tools_kwargs": true,
"question": "Given real numbers $x$ and $y$ satisfying the equation of curve $C$: $x^{2}+y^{2}-2x-2=0$, which of the following options is correct?\n\nA: The maximum value of $x^{2}+y^{2}$ is $\\sqrt{3}+1$\n\nB: The maximum value of $\\frac{y+1}{x+1}$ is $2+\\sqrt{6}$\n\nC: The minimum value of $|x-y+3|$ is $2\\sqrt{2}-\\sqrt{3}$\n\nD: A tangent line is drawn through the point $(0, \\sqrt{2})$ on curve $C$, then the equation of the tangent line is $x-\\sqrt{2}y+2=0$",
"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": 2056,
"need_tools_kwargs": true,
"question": "给定非负实数 \\(\\alpha\\)。求 \\(\\lambda = \\lambda(\\alpha)\\) 的最小整数值，使得对任意复数 \\(z_{1}\\), \\(z_{2}\\) 和实数 \\(x \\in [0,1]\\)，若 \\(|z_{1}| \\leqslant \\alpha|z_{1}-z_{2}|\\)，则 \\(|z_{1}-x z_{2}| \\leqslant \\lambda|z_{1}-z_{2}|\\)。请给出最小整数值的答案。",
"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": 2057,
"need_tools_kwargs": true,
"question": "Do both films Thanks For Sharing and The Unsaid have the directors that share 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": "240",
"style": "rule"
} | {
"index": 2058,
"need_tools_kwargs": true,
"question": "Given that $a, b, c$ are positive integers satisfying $$a+b+c=\\operatorname{gcd}(a, b)+\\operatorname{gcd}(b, c)+\\operatorname{gcd}(c, a)+120$$ determine the maximum possible value of $a$.",
"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": "126",
"style": "rule"
} | {
"index": 2059,
"need_tools_kwargs": true,
"question": "Given an increasing sequence of 8 real numbers, Diana listed all possible sequences of 4 consecutive numbers. It turned out that two of the five new sequences are arithmetic progressions with common differences of 4 and 36, respectively, and one of the sequences is a geometric progression. Find the largest of the given 8 numbers. Mention all possible options.",
"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": "60.375",
"style": "rule"
} | {
"index": 2060,
"need_tools_kwargs": true,
"question": "Each of the lateral edges of a pyramid is equal to 269/32. The base of the pyramid is a triangle with sides 13, 14, 15. Find the volume of the pyramid.",
"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": "967",
"style": "rule"
} | {
"index": 2061,
"need_tools_kwargs": true,
"question": "Points $A$, $B$, $C$, $D$, and $E$ are on the same plane such that $A,E,C$ lie on a line in that order, $B,E,D$ lie on a line in that order, $AE = 1$, $BE = 4$, $CE = 3$, $DE = 2$, and $\\angle AEB = 60^\\circ$. Let $AB$ and $CD$ intersect at $P$. The square of the area of quadrilateral $PAED$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?",
"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": "(1, \\frac{4}{3}]",
"style": "rule"
} | {
"index": 2062,
"need_tools_kwargs": true,
"question": "Given \\( x, y, z \\in (0,1) \\) and \\( x+y+z = 2 \\), the range of values for \\( xy + yz + zx \\) is ( ).\n\n(A) \\(\\left(0, \\frac{4}{3}\\right]\\) \n(B) \\(\\left(1, \\frac{4}{3}\\right]\\) \n(C) \\(\\left(1, \\frac{4}{3}\\right]\\) \n(D) \\(\\left(\\frac{4}{3}, 2\\right]\\)\n\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... | qa | {
"ground_truth": "Buenos Aires",
"style": "rule"
} | {
"index": 2063,
"need_tools_kwargs": true,
"question": "Where did the director of film Detective (1954 Film) 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... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"index": 2064,
"need_tools_kwargs": true,
"question": "Convert the fraction \\(\\frac{123456789}{2^{26} \\times 5^{4}}\\) to a decimal and determine how many decimal places the resulting number has.",
"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": "27",
"style": "rule"
} | {
"index": 2065,
"need_tools_kwargs": true,
"question": "Find $PQ$ in the triangle below.\n\n\n[asy]\nunitsize(1inch);\npair P,Q,R;\nP = (0,0);\nQ= (sqrt(3),0);\nR = (0,1);\ndraw (P--Q--R--P,linewidth(0.9));\ndraw(rightanglemark(Q,P,R,3));\nlabel(\"$P$\",P,S);\nlabel(\"$Q$\",Q,S);\nlabel(\"$R$\",R,N);\nlabel(\"$9\\sqrt{3}$\",R/2,W);\nlabel(\"$30^\\circ$\",(1.25,0),N);\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": "1990",
"style": "rule"
} | {
"index": 2066,
"need_tools_kwargs": true,
"question": "In what year was the singer-songwriter who did the duet \"I Wanna Know You\" with Hannah Montana 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": "5, 1",
"style": "rule"
} | {
"index": 2067,
"need_tools_kwargs": true,
"question": "Find all real solutions to\n\\[\n\\frac{1}{(x - 1)(x - 2)} + \\frac{1}{(x - 2)(x - 3)} + \\frac{1}{(x - 3)(x - 4)} + \\frac{1}{(x - 4)(x - 5)} = \\frac{1}{4}.\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... | qa | {
"ground_truth": "Versailles",
"style": "rule"
} | {
"index": 2068,
"need_tools_kwargs": true,
"question": "Where was the place of death of Louise Diane D'Orléans'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": "22",
"style": "rule"
} | {
"index": 2069,
"need_tools_kwargs": true,
"question": "Determine how many unordered pairs of edges of a given square pyramid can be selected such that they define a plane.",
"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": "Jonathan Mark Buckland",
"style": "rule"
} | {
"index": 2070,
"need_tools_kwargs": true,
"question": "Who is the lead guitarist and co-founder with Chris martin of the band formerly known as Pectoralz, which was renamed Coldplay?",
"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": "Rock and Roll Hall of Fame",
"style": "rule"
} | {
"index": 2071,
"need_tools_kwargs": true,
"question": "What is the award that the performer of song Mistreated (Song) earned?",
"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": "22",
"style": "rule"
} | {
"index": 2072,
"need_tools_kwargs": true,
"question": "\"The Injury\" was one of how many episodes that season?",
"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 November 1985",
"style": "rule"
} | {
"index": 2073,
"need_tools_kwargs": true,
"question": "When did the director of film By The Lake 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... | math | {
"ground_truth": "\\left( -\\infty, -\\frac{1}{5} \\right)",
"style": "rule"
} | {
"index": 2074,
"need_tools_kwargs": true,
"question": "Find all values of $k$ so that the domain of\n\\[b(x) = \\frac{kx^2 + 2x - 5}{-5x^2 + 2x + k}\\]is the set of all real numbers.",
"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": "12.6491106406735",
"style": "rule"
} | {
"index": 2075,
"need_tools_kwargs": true,
"question": "In triangle $ABC$, $AB = 9$, $BC = 12$, $AC = 15$, and $CD$ is the angle bisector. Find the length of $CD$.",
"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": "a \\geq 1",
"style": "rule"
} | {
"index": 2076,
"need_tools_kwargs": true,
"question": "Given the equation \\( |x| = a x + 1 \\) has a negative root and no positive root, determine the range of \\( a \\).\n(A) \\( a > -1 \\).\n(B) \\( a = 1 \\).\n(C) \\( a \\geqslant 1 \\).\n(D) None of the above.\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": "6066",
"style": "rule"
} | {
"index": 2077,
"need_tools_kwargs": true,
"question": "已知数列$\\left\\{a_n\\right\\}$满足：$$a_0=\\sqrt{6}\\:,a_{n+1}=\\left[\\:a_n\\:\\right]+\\frac{1}{\\left\\{\\:a_n\\:\\right\\}}\\:,$$其中，$[a]$表示不超过实数 $a$ 的最大整数，$\\{$ $a$ $\\} = a$ -[ $a$ ].则 $a_{2\\:020}=$. 请给出整数部分与根号下数值的和。",
"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": "Graceland",
"style": "rule"
} | {
"index": 2078,
"need_tools_kwargs": true,
"question": "Where did the performer of song If Every Day Was Like Christmas 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... | math | {
"ground_truth": "[4-2 \\sqrt {5},4+2 \\sqrt {5}]",
"style": "rule"
} | {
"index": 2079,
"need_tools_kwargs": true,
"question": "In the Cartesian coordinate system $xOy$, the general equation of circle $C$ is $x^{2}+y^{2}-4x-6y+12=0$. In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the polar equation of line $l$ is $\\rho\\sin (\\theta+ \\frac {\\pi}{4})= \\sqrt {2}$. \n(Ⅰ) Write the parametric equation of circle $C$ and the Cartesian equation of line $l$; \n(Ⅱ) Suppose the intersection points of line $l$ with the $x$-axis and $y$-axis are $A$ and $B$ respectively, and $P$ is any point on circle $C$. Find the range of values for $\\overrightarrow{PA}\\cdot \\overrightarrow{PB}$.",
"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": "10",
"style": "rule"
} | {
"index": 2080,
"need_tools_kwargs": true,
"question": "Let $\\alpha,\\beta,$ and $\\gamma$ be three real numbers. Suppose that \n$$\\cos\\alpha+\\cos\\beta+\\cos\\gamma=1$$\n$$\\sin\\alpha+\\sin\\beta+\\sin\\gamma=1.$$\nFind the smallest possible value of $\\cos \\alpha$. The original answer is in the format \\frac{k-\\sqrt{m}}{n}, please provide the value of k + 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": "m=2 \\quad 3 * 12 = \\frac{24}{7}",
"style": "rule"
} | {
"index": 2081,
"need_tools_kwargs": true,
"question": "For any two numbers \\( x \\) and \\( y \\), the operation \"*\" is defined as:\n\\[ x * y = \\frac{4 \\times x \\times y}{m \\times x + 3 \\times y} \\]\n(where \\( m \\) is a constant value). If \\( 1 * 2 = 1 \\), find the value of \\( m \\). Additionally, calculate \\( 3 * 12 \\).",
"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": "EA Tiburon",
"style": "rule"
} | {
"index": 2082,
"need_tools_kwargs": true,
"question": "Which company developed this American football video game series whose engine was used for Mutant League Football?",
"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 War of Independence",
"style": "rule"
} | {
"index": 2083,
"need_tools_kwargs": true,
"question": "What other name is the war, where the Great Chain at Battery Cove during, known as?",
"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": "0.2647058823529412",
"style": "rule"
} | {
"index": 2084,
"need_tools_kwargs": true,
"question": "I have a drawer with 6 forks, 6 spoons, and 6 knives in it. If I reach in and randomly remove three pieces of silverware, what is the probability that I get one fork, one spoon, and one knife?",
"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{13}{8}",
"style": "rule"
} | {
"index": 2085,
"need_tools_kwargs": true,
"question": "Determine the exact value of\n\\[\\sqrt{\\left( 2 - \\sin^2 \\frac{\\pi}{7} \\right) \\left( 2 - \\sin^2 \\frac{2 \\pi}{7} \\right) \\left( 2 - \\sin^2 \\frac{3 \\pi}{7} \\right)}.\\]",
"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": "Damon Beesley and Iain Morris.",
"style": "rule"
} | {
"index": 2086,
"need_tools_kwargs": true,
"question": "Who wrote the comedy show which used the song Moving to New York as its end credits 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... | math | {
"ground_truth": "841",
"style": "rule"
} | {
"index": 2087,
"need_tools_kwargs": true,
"question": "Let $x_1\\leq x_2\\leq \\cdots\\leq x_{100}$ be real numbers such that $|x_1| + |x_2| + \\cdots + |x_{100}| = 1$ and $x_1 + x_2 + \\cdots + x_{100} = 0$. Among all such $100$-tuples of numbers, the greatest value that $x_{76} - x_{16}$ can achieve is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.",
"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... | qa | {
"ground_truth": "John Y. Brown, Jr.",
"style": "rule"
} | {
"index": 2088,
"need_tools_kwargs": true,
"question": "Who, in 1978, acquired ownership of the NBA team that plays their home games at TD Garden?",
"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": "Ben Chandler",
"style": "rule"
} | {
"index": 2089,
"need_tools_kwargs": true,
"question": "Who served as a congressman for the the district which contains the cities of Lexington (including its suburbs), Richmond, and Frankfort, the state capital?",
"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": "4ab",
"style": "rule"
} | {
"index": 2090,
"need_tools_kwargs": true,
"question": "$F$ is a convex figure with two mutually perpendicular axes of symmetry. Through a point $M$ located inside the figure and at distances $a$ and $b$ from the axes, lines parallel to the axes are drawn. These lines divide $F$ into four regions. Find the difference between the sum of the areas of the larger and smaller regions and the sum of the areas of the other two regions.",
"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": "11",
"style": "rule"
} | {
"index": 2091,
"need_tools_kwargs": true,
"question": "In airspace, there are clouds. It turns out that it is possible to divide the space into parts using ten planes so that there is no more than one cloud in each part. What is the maximum number of clouds that an airplane could fly through while adhering to a straight-line course?",
"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": "Advait Chandan",
"style": "rule"
} | {
"index": 2092,
"need_tools_kwargs": true,
"question": "Who directed the movie that the Indian actress who debuted in Dangal appeared in with Meher Vij and Aamir Khan?",
"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": "January 22, 1950",
"style": "rule"
} | {
"index": 2093,
"need_tools_kwargs": true,
"question": "When did the director of film Rubber Tires 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": "Janet Jackson",
"style": "rule"
} | {
"index": 2094,
"need_tools_kwargs": true,
"question": "Matthew Felker acts alongside a dancer who began her career with what singer?",
"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": "45",
"style": "rule"
} | {
"index": 2095,
"need_tools_kwargs": true,
"question": "in a class , 20 % of the students were absent for an exam . 30 % failed by 20 marks and 10 % just passed . find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40 .",
"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": 2096,
"need_tools_kwargs": true,
"question": "A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. What is this positive integer?",
"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": 2097,
"need_tools_kwargs": true,
"question": "What country of origin does Ford World Headquarters and The Henry Ford 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... | qa | {
"ground_truth": "Seoul Records",
"style": "rule"
} | {
"index": 2098,
"need_tools_kwargs": true,
"question": "Lee Hae-in is a part of the girl group formed by the company that was formerly known as what?",
"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": 2099,
"need_tools_kwargs": true,
"question": "Let \\( x \\) be a positive integer, and write \\( a = \\left\\lfloor \\log_{10} x \\right\\rfloor \\) and \\( b = \\left\\lfloor \\log_{10} \\frac{100}{x} \\right\\rfloor \\). Here \\( \\lfloor c \\rfloor \\) denotes the greatest integer less than or equal to \\( c \\). Find the largest possible value of \\( 2a^2 - 3b^2 \\).",
"split": "train"
} | null |
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