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aime2025
[ { "role": "user", "content": "Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\n\nLet's think step by step and output the final answer within \\boxed{}." } ]
math
{ "style": "rule", "ground_truth": "70" }
{ "split": "test", "index": 0, "answer": "70", "question": "Find the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$." }
single_turn_agent
aime2025
[ { "role": "user", "content": "On $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be ...
math
{ "style": "rule", "ground_truth": "588" }
{ "split": "test", "index": 1, "answer": "588", "question": "On $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ t...
single_turn_agent
aime2025
[ { "role": "user", "content": "The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of ...
math
{ "style": "rule", "ground_truth": "16" }
{ "split": "test", "index": 2, "answer": "16", "question": "The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was g...
single_turn_agent
aime2025
[ { "role": "user", "content": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\n\nLet's think step by step and output the final answer within \\boxed{}." } ]
math
{ "style": "rule", "ground_truth": "117" }
{ "split": "test", "index": 3, "answer": "117", "question": "Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$." }
single_turn_agent
aime2025
[ { "role": "user", "content": "There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\n\nLet's think step by step and output the final answer wit...
math
{ "style": "rule", "ground_truth": "279" }
{ "split": "test", "index": 4, "answer": "279", "question": "There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025." }
single_turn_agent
aime2025
[ { "role": "user", "content": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\n\nLet's think step by s...
math
{ "style": "rule", "ground_truth": "504" }
{ "split": "test", "index": 5, "answer": "504", "question": "An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}...
single_turn_agent
aime2025
[ { "role": "user", "content": "The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possi...
math
{ "style": "rule", "ground_truth": "821" }
{ "split": "test", "index": 6, "answer": "821", "question": "The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabeti...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{...
math
{ "style": "rule", "ground_truth": "77" }
{ "split": "test", "index": 7, "answer": "77", "question": "Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. F...
single_turn_agent
aime2025
[ { "role": "user", "content": "The parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive inte...
math
{ "style": "rule", "ground_truth": "62" }
{ "split": "test", "index": 8, "answer": "62", "question": "The parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$,...
single_turn_agent
aime2025
[ { "role": "user", "content": "The 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzz...
math
{ "style": "rule", "ground_truth": "81" }
{ "split": "test", "index": 9, "answer": "81", "question": "The 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first t...
single_turn_agent
aime2025
[ { "role": "user", "content": "A piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(...
math
{ "style": "rule", "ground_truth": "259" }
{ "split": "test", "index": 10, "answer": "259", "question": "A piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$...
single_turn_agent
aime2025
[ { "role": "user", "content": "The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in...
math
{ "style": "rule", "ground_truth": "510" }
{ "split": "test", "index": 11, "answer": "510", "question": "The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finit...
single_turn_agent
aime2025
[ { "role": "user", "content": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and conne...
math
{ "style": "rule", "ground_truth": "204" }
{ "split": "test", "index": 12, "answer": "204", "question": "Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in d...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive in...
math
{ "style": "rule", "ground_truth": "60" }
{ "split": "test", "index": 13, "answer": "60", "question": "Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where ...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\n\nLet's think step by step and output the final answer within \\boxed{}." } ]
math
{ "style": "rule", "ground_truth": "735" }
{ "split": "test", "index": 14, "answer": "735", "question": "Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$." }
single_turn_agent
aime2025
[ { "role": "user", "content": "Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\n\nLet's thin...
math
{ "style": "rule", "ground_truth": "468" }
{ "split": "test", "index": 15, "answer": "468", "question": "Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\t...
single_turn_agent
aime2025
[ { "role": "user", "content": "Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\n\nLet's think step by step and output the final answer within \\boxed{}." } ]
math
{ "style": "rule", "ground_truth": "49" }
{ "split": "test", "index": 16, "answer": "49", "question": "Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $." }
single_turn_agent
aime2025
[ { "role": "user", "content": "Four unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\n\nLet's think step by step and...
math
{ "style": "rule", "ground_truth": "82" }
{ "split": "test", "index": 17, "answer": "82", "question": "Four unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings." }
single_turn_agent
aime2025
[ { "role": "user", "content": "The product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965}...
math
{ "style": "rule", "ground_truth": "106" }
{ "split": "test", "index": 18, "answer": "106", "question": "The product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^...
single_turn_agent
aime2025
[ { "role": "user", "content": "Suppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $...
math
{ "style": "rule", "ground_truth": "336^\\circ" }
{ "split": "test", "index": 19, "answer": "336^\\circ", "question": "Suppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, ...
single_turn_agent
aime2025
[ { "role": "user", "content": "Circle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangl...
math
{ "style": "rule", "ground_truth": "293" }
{ "split": "test", "index": 20, "answer": "293", "question": "Circle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are rela...
math
{ "style": "rule", "ground_truth": "237" }
{ "split": "test", "index": 21, "answer": "237", "question": "Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, wh...
single_turn_agent
aime2025
[ { "role": "user", "content": "From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest...
math
{ "style": "rule", "ground_truth": "610" }
{ "split": "test", "index": 22, "answer": "610", "question": "From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively c...
single_turn_agent
aime2025
[ { "role": "user", "content": "There are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\n\nLet's think step by step and output the fin...
math
{ "style": "rule", "ground_truth": "149" }
{ "split": "test", "index": 23, "answer": "149", "question": "There are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $." }
single_turn_agent
aime2025
[ { "role": "user", "content": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\n\nLet's think step ...
math
{ "style": "rule", "ground_truth": "907" }
{ "split": "test", "index": 24, "answer": "907", "question": "Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided b...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\n\nLet's think step by step and output the final answer within \\boxed{}." } ]
math
{ "style": "rule", "ground_truth": "113" }
{ "split": "test", "index": 25, "answer": "113", "question": "Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments." }
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of...
math
{ "style": "rule", "ground_truth": "19" }
{ "split": "test", "index": 26, "answer": "19", "question": "Let $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\le...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $...
math
{ "style": "rule", "ground_truth": "248" }
{ "split": "test", "index": 27, "answer": "248", "question": "Let the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime posit...
single_turn_agent
aime2025
[ { "role": "user", "content": "Let $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some posit...
math
{ "style": "rule", "ground_truth": "104" }
{ "split": "test", "index": 28, "answer": "104", "question": "Let $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ ...
single_turn_agent
aime2025
[ { "role": "user", "content": "There are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of...
math
{ "style": "rule", "ground_truth": "240" }
{ "split": "test", "index": 29, "answer": "240", "question": "There are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the ...
single_turn_agent

Multi-Domain RLVR Evaluation Suite

The eight benchmarks reported in the paper, converted to the verl RLHF parquet schema so they can be scored directly by verl.trainer.main_ppo in val_only mode. The matching training data is in the companion LLM-Fusion-Train dataset.

Subsets

Subset Domain Rows Size
AIME2025 Math 30 0.0 MiB
AIME2026 Math 30 0.0 MiB
GPQA Science 198 0.1 MiB
LCB_v5 Code 167 390.4 MiB
LCB_v6 Code 175 92.3 MiB
IFEval IF 541 0.1 MiB
IFBench IF 300 0.1 MiB
BFCL_v3 Agent 200 0.1 MiB

Each benchmark is a separate config holding a single test split. They cannot be splits of one config because extra_info differs per benchmark.

Every row carries an agent_name column that tells verl's rollout which agent loop to use: tool_agent for BFCL_v3, whose tasks are multi-turn tool calling, and single_turn_agent for the other seven.

LCB_v5 and LCB_v6 are large for their row counts because the unit tests are embedded in reward_model.ground_truth; scoring them needs a running SandboxFusion server.

Upstream benchmarks

Subset Upstream
AIME2025, AIME2026 American Invitational Mathematics Examination
GPQA GPQA (Diamond)
LCB_v5, LCB_v6 LiveCodeBench
IFEval Google IFEval
IFBench AllenAI IFBench
BFCL_v3 Berkeley Function Calling Leaderboard v3, multi-turn category

Only the prompts and grading targets are redistributed here, in verl's schema. Refer to each benchmark's own terms of use.

Usage

from datasets import load_dataset

aime = load_dataset("<repo-id>", "AIME2025", split="test")
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Collection including Siye01/LLM-Fusion-Test