conversations listlengths 2 2 | question stringlengths 8 1.83k | source null | id null | prompt listlengths 2 2 | answer stringclasses 522
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
value | task_config stringclasses 1
value | model_responses__example_annotation listlengths 1 1 | model_responses__example_annotation__eval_is_correct listlengths 1 1 | model_responses__example_annotation__eval_extracted_answers listlengths 1 1 | prompt_type stringclasses 2
values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Prove that\n\n$$\n\\operatorname{tg} 9^{\\circ}-\\operatorname{tg} 27^{\\circ}-\\operatorname{tg} 63^{\\circ}+\\operatorname{tg} 81^{\\circ}=4\n$$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to prove that tan9° minus tan27° minus tan63° plus tan81° e... | Prove that
$$
\operatorname{tg} 9^{\circ}-\operatorname{tg} 27^{\circ}-\operatorname{tg} 63^{\circ}+\operatorname{tg} 81^{\circ}=4
$$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 4 | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"To prove the given identity:\n\n\\[ \\operatorname{tg} 9^\\circ - \\operatorname{tg} 27^\\circ - \\operatorname{tg} 63^\\circ + \\operatorname{tg} 81^\\circ = 4 \\]\n\nwe can start by considering the properties of tangent functions and their relationships.\n\n**Step 1: Simplify Using Tangent Identities**\n\nWe kno... | [
true
] | [
"4"
] | alternative_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer by carefully examining each step of the model response.\n\n1. **Simplification Using Tangent Identities**: The model correctly uses the co-function identity to transform the tangents into cotangents.\n2. **Cotangent Identity Application**: The model correctly applies the identity \\(\\cot... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "Prove that\n\n$$\n\\operatorname{tg} 9^{\\circ}-\\operatorname{tg} 27^{\\circ}-\\operatorname{tg} 63^{\\circ}+\\operatorname{tg} 81^{\\circ}=4\n$$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to prove that tan9° minus tan27° minus tan63° plus tan81° e... | Prove that
$$
\operatorname{tg} 9^{\circ}-\operatorname{tg} 27^{\circ}-\operatorname{tg} 63^{\circ}+\operatorname{tg} 81^{\circ}=4
$$ | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 4 | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"To prove the given identity, let's start by examining the tangent values of the angles involved:\n\nFirstly, we know:\n\\[ \\tan(81^\\circ) = \\cot(9^\\circ) \\]\nand \n\\[ \\tan(63^\\circ) = \\cot(27^\\circ). \\]\n\nUsing these identities, we can rewrite the expression as:\n\\[ \\tan 9^\\circ - \\tan 27^\\circ - ... | [
true
] | [
"4"
] | alternative_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer by rechecking the steps taken in the model response. The model response correctly identified several key trigonometric identities and used them appropriately. It transformed the original expression using co-function identities and simplified it using known tangent-cotangent relationships.... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}$, then $\\angle B = \\_\\_\\_\\_\\_\\_$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to find angle B in triangle ABC. The problem says that an... | In triangle $\triangle ABC$, if $\angle B = \angle A + 20^{\circ}$ and $\angle C = 50^{\circ}$, then $\angle B = \_\_\_\_\_\_$. | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 75^\circ | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}$, find $\\angle B$.\n\nStep 1: Recall that the sum of angles in a triangle is $180^{\\circ}$. Therefore, we have:\n\\[\n\\angle A + \\angle B + \\angle C = 180^{\\circ}\n\\]\n\nStep 2: Substitute... | [
false
] | [
"75^{\\circ}"
] | rephrase_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly set up the equation and solved for angle A, finding that angle A is 55°. It then used the relationship between angle A and angle B to find that angle B is 75°. The solution also verified that the sum of the angles is 180°, confirming the correctness of the individual ... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.218:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vllm... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and (...TRUNCATED) | "In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 75^\circ | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\(...TRUNCATED) | [
false
] | [
"75^{\\circ}"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The solution follows the standard procedure for solving such problems i(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and (...TRUNCATED) | "In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 75^\circ | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Given the angles in triangle \\( \\triangle ABC \\), we know:\n\\[ \\angle B = \\angle A + 20^\\ci(...TRUNCATED) | [
true
] | [
"75^\\circ"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly set up the equation based on the given information (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and (...TRUNCATED) | "In triangle $\\triangle ABC$, if $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 75^\circ | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Given that $\\angle B = \\angle A + 20^{\\circ}$ and $\\angle C = 50^{\\circ}$ in $\\triangle ABC$(...TRUNCATED) | [
true
] | [
"75^\\circ"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly set up the equations based on the given information(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x(...TRUNCATED) | Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x)$ is an odd function. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given the function \\( f(x) = x(x-1)(x+a) \\), find the value of \\( a \\) suc(...TRUNCATED) | [
true
] | [
"1"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identifies the process of determining the (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x(...TRUNCATED) | Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x)$ is an odd function. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Given the function \\( f(x) = x(x-1)(x+a) \\), find the value of \\( a \\) suc(...TRUNCATED) | [
true
] | [
"1"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model response correctly identifies the process required to determi(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x(...TRUNCATED) | Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x)$ is an odd function. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the value of \\(a\\) such that \\(f(x) = x(x-1)(x+a)\\) is an odd function, we need t(...TRUNCATED) | [
true
] | [
"1"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer. The model correctly followed the steps to determine that for \\(f(x) = (...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x(...TRUNCATED) | Given the function $f(x)=x(x-1)(x+a)$, find the value of $a$ such that $f(x)$ is an odd function. | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 1 | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["To determine the value of \\(a\\) such that \\(f(x) = x(x-1)(x+a)\\) is an odd function, we need t(...TRUNCATED) | [
true
] | [
"1"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer by checking if the function \\( f(x) = x(x-1)(x+1) \\) is indeed odd whe(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.218:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4