problem stringlengths 166 1.26k | answer stringlengths 1 1.69k | subject stringclasses 1
value | dataset_metadata stringlengths 609 35.2k | model_metrics dict | anthropic_index_category stringclasses 21
values |
|---|---|---|---|---|---|
Question: Compute the value of the expression \(\frac{1-\log_a^{3}{b}}{(\log_a b + \log_b a + 1)\log_a\frac{a}{b}}\) using logarithmic properties and algebraic manipulations. Show all steps and simplify the expression to its most basic form.
Please solve this step by step, then output your answer on a new line as 'The... | \(\log_a b\) | natural_reasoning | {"question": "Compute the value of the expression \\(\\frac{1-\\log_a^{3}{b}}{(\\log_a b + \\log_b a + 1)\\log_a\\frac{a}{b}}\\) using logarithmic properties and algebraic manipulations. Show all steps and simplify the expression to its most basic form.", "reference_answer": "\\(\\log_a b\\)", "responses": [{"response_... | {
"allenai/Olmo-3-32B-Think": {
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"per_query_joules": 2279.3218929122136,
"total_joules": 787740.5510490038
},
"evaluation": {
"config": {
"batch_size": 512,
"dtype... | Computer and mathematical |
Question: Design a system to recharge batteries using ambient electromagnetic energy from the atmosphere, considering technical challenges and feasibility.
Please solve this step by step, then output your answer on a new line as 'The answer is: X' | It is theoretically possible but practically challenging due to low power density. | natural_reasoning | {"question": "Design a system to recharge batteries using ambient electromagnetic energy from the atmosphere, considering technical challenges and feasibility.", "reference_answer": "It is theoretically possible but practically challenging due to low power density.", "responses": [{"response_model": "Llama-3.3-70B-Inst... | {
"allenai/Olmo-3-32B-Think": {
"compute_metrics": {
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"per_query_joules": 574.0018607175537,
"total_joules": 281592.63344713213
},
"evaluation": {
"config": {
"batch_size": 512,
"dtype... | Architecture and engineering |
Question: Prove that for functions $f$, $g$: $\mathbb{N} \to \mathbb{R}$, $f \in O(g)$ if and only if $\limsup_{n\to\infty}|\frac{f(n)}{g(n)}| < \infty$. Use the definition of $O$ notation and provide a rigorous proof.
Please solve this step by step, then output your answer on a new line as 'The answer is: X' | f \in O(g) \Longleftrightarrow \limsup_{n\to\infty}|\frac{f(n)}{g(n)}| < \infty | natural_reasoning | {"question": "Prove that for functions $f$, $g$: $\\mathbb{N} \\to \\mathbb{R}$, $f \\in O(g)$ if and only if $\\limsup_{n\\to\\infty}|\\frac{f(n)}{g(n)}| < \\infty$. Use the definition of $O$ notation and provide a rigorous proof.", "reference_answer": "f \\in O(g) \\Longleftrightarrow \\limsup_{n\\to\\infty}|\\frac{f... | {
"allenai/Olmo-3-32B-Think": {
"compute_metrics": {
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"per_query_joules": 2105.432455363732,
"total_joules": 747767.8531243306
},
"evaluation": {
"config": {
"batch_size": 512,
"dtype"... | Computer and mathematical |
Question: Given the problem of finding the sum over all compositions of a number $n$ into $3$ parts of the product of those parts, use generating functions to derive a formula for $f(n)$, where $f(n)$ represents this sum. Provide a step-by-step explanation of your approach and calculate $f(5)$ as an example.
Please so... | The coefficients of $\frac{x^3}{(1-x)^6}$ | natural_reasoning | {"question": "Given the problem of finding the sum over all compositions of a number $n$ into $3$ parts of the product of those parts, use generating functions to derive a formula for $f(n)$, where $f(n)$ represents this sum. Provide a step-by-step explanation of your approach and calculate $f(5)$ as an example.", "ref... | {
"allenai/Olmo-3-32B-Think": {
"compute_metrics": {
"flops_per_request": 0,
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"energy_metrics": {
"per_query_joules": 2118.9159936130977,
"total_joules": 750956.7680568272
},
"evaluation": {
"config": {
"batch_size": 512,
"dtype... | Computer and mathematical |
"Question: Explain why white shirts washed in blue appear brighter, considering the principles of co(...TRUNCATED) | "The bluing effect is due to the absorption of ultraviolet light and emission of bluish light by fab(...TRUNCATED) | natural_reasoning | "{\"question\": \"Explain why white shirts washed in blue appear brighter, considering the principle(...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Life, physical, and social science |
"Question: Given the joint distribution of discrete random variables X and Y as follows: ... Find E((...TRUNCATED) | "The correct calculations yield specific values for E(XY), Cov(X,Y), and correlation(X,Y) based on t(...TRUNCATED) | natural_reasoning | "{\"question\": \"Given the joint distribution of discrete random variables X and Y as follows: ... (...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Computer and mathematical |
"Question: Given that flipping a coin is an independent event, explain why simply adding the probabi(...TRUNCATED) | 1/2 + 1/2 - 1/4 = 3/4 | natural_reasoning | "{\"question\": \"Given that flipping a coin is an independent event, explain why simply adding the (...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Computer and mathematical |
"Question: Given a character table for a finite group G, explain how to determine the kernel of each(...TRUNCATED) | "The kernel of a character χ can be found by identifying the conjugacy classes corresponding to the(...TRUNCATED) | natural_reasoning | "{\"question\": \"Given a character table for a finite group G, explain how to determine the kernel (...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Life, physical, and social science |
"Question: Let $G$ be a polycyclic group and $N$ a normal subgroup of $G$. Define $h(G)$ as the Hirs(...TRUNCATED) | h(G) = h(N) + h(G/N) | natural_reasoning | "{\"question\": \"Let $G$ be a polycyclic group and $N$ a normal subgroup of $G$. Define $h(G)$ as t(...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Computer and mathematical |
"Question: A 16 g rifle bullet traveling 180 m/s buries itself in a 4.0 kg pendulum hanging on a 3.5(...TRUNCATED) | 0.0262 m | natural_reasoning | "{\"question\": \"A 16 g rifle bullet traveling 180 m/s buries itself in a 4.0 kg pendulum hanging o(...TRUNCATED) | {"allenai/Olmo-3-32B-Think":{"compute_metrics":{"flops_per_request":0.0,"macs_per_request":0.0},"ene(...TRUNCATED) | Architecture and engineering |
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