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* add agenteval-notebook for math problems and the blog post about it * update gitignore * updates to notebook * adding folder for the logs * adding math problems logs * adding folder for alfworld logs * added limitiation and future work to blog post * minor edits blog post * adding changes * reorg * modify the main notebook * modification of the main notebook * remove wrong notebook * uploading new notebook * update agenteval notebook * change the sample * Update agenteval_cq_math.ipynb * adding final changes to notebook * updated framework picture * Update index.mdx * Update index.md * Add files via upload * updates to notebool * revise the blog * revise the blog * update the agent img * revise the blog * revise the blog * Excluded model logs from the main branch, you can find them in agenteval branch * Fixed pre-commit formatting. * Update website/blog/2023-11-11-AgentEval/index.mdx Co-authored-by: Chi Wang <wang.chi@microsoft.com> * update gitignore * update index.mdx * update authors.yml by adding Negar and Julia * remove md file * remove md file * update gitignore * update authors file * pre-commit checks * pre-commit checks on authors.yml * pre-commit checks on authors.yml * update index.mdx * update authors.yml by adding Negar and Julia * updated the blog-post version 1 * updated the blog-post: TL;DR is ready * updated the blog-post: first part of introduction is ready * updated figures: typos on fig 1, changed terminology on the fig 2 * upadated the Framework part * fixed redering issues * upload zip file instead of single samples * update prealgebra.zip * update * upload * update z * update naming * update zip * update the agenteval notebook * update the notebook - removing unmercenary logs * updated fig 1 and references to it * updated fig 1 * incorporated PR comments * merged agenteval branch * final changes to the blog * updated taxonomy * update notebook * minor changes to the blog * Fixed formatting * Update the link in agenteval_cq_math.ipynb * update the blog and link in notebook * Update index.mdx * change folder name * Changes to be committed: modified: OAI_CONFIG_LIST_sample.txt * add sample OAI file * fix the url link to colab and typos * fix the url link to colab and typos * add authors * update profile pic * "update authors" * fixing the problem in test_groupchat.py * update the title lower case * reverting changes in setup.py * rerun pre-commit --------- Co-authored-by: Negar Arabzadeh <ngr.arabzadeh@gmail.com> Co-authored-by: Julia Kiseleva <jukisele@microsoft.com> Co-authored-by: afourney <adamfo@microsoft.com> Co-authored-by: Chi Wang <wang.chi@microsoft.com> Co-authored-by: Qingyun Wu <qingyun.wu@psu.edu>
25 lines
2.6 KiB
JSON
25 lines
2.6 KiB
JSON
{
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"problem": "Find $24^{-1} \\pmod{11^2}$. That is, find the residue $b$ for which $24b \\equiv 1\\pmod{11^2}$.\n\nExpress your answer as an integer from $0$ to $11^2-1$, inclusive.",
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"level": "Level 5",
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"type": "Number Theory",
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"solution": "Since $5 \\times 24 = 120 = 121 - 1$, it follows that $-5 \\times 24 \\equiv 1 \\pmod{121}$. Adding 121 to $-5$ to make it positive, we find $(-5 + 121) \\times 24 \\equiv 116 \\times 24 \\equiv 1 \\pmod{121}$, so it follows that the modular inverse of $24$ is $\\boxed{116}$ when taken modulo $121$.",
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"correct_ans": "116",
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"problem_id": "5",
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"response_with_ans": "To find the modular inverse of 24 modulo 11^2, we can use the Extended Euclidean Algorithm. Here is a Python function to compute the modular inverse using this algorithm:\n\n```python\ndef mod_inverse(a, m):\n g, x, _ = extended_gcd(a, m)\n if g != 1:\n raise Exception(f\"{a} and {m} are not coprime.\")\n return x % m\n\ndef extended_gcd(a, b):\n if a == 0:\n return b, 0, 1\n else:\n g, x, y = extended_gcd(b % a, a)\n return g, y - (b // a) * x, x\n```\n\nLet's use the above function to find the modular inverse of 24 modulo 11^2:\n\n```python\na = 24\nm = 11**2\nmod_inverse(a, m)\n```\n\nI will execute the above code to find the modular inverse of 24 modulo 11^2.",
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"round": 0,
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"messages": [
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{
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"content": "Find $24^{-1} \\pmod{11^2}$. That is, find the residue $b$ for which $24b \\equiv 1\\pmod{11^2}$.\n\nExpress your answer as an integer from $0$ to $11^2-1$, inclusive.",
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"role": "user"
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},
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{
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"content": "To find the modular inverse of 24 modulo 11^2, we can use the Extended Euclidean Algorithm. Here is a Python function to compute the modular inverse using this algorithm:\n\n```python\ndef mod_inverse(a, m):\n g, x, _ = extended_gcd(a, m)\n if g != 1:\n raise Exception(f\"{a} and {m} are not coprime.\")\n return x % m\n\ndef extended_gcd(a, b):\n if a == 0:\n return b, 0, 1\n else:\n g, x, y = extended_gcd(b % a, a)\n return g, y - (b // a) * x, x\n```\n\nLet's use the above function to find the modular inverse of 24 modulo 11^2:\n\n```python\na = 24\nm = 11**2\nmod_inverse(a, m)\n```\n\nI will execute the above code to find the modular inverse of 24 modulo 11^2.",
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"role": "assistant"
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}
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],
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"time": 13.481226921081543,
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"check_result": "let me verify the modular inverse of 24 modulo 11^2.\n\nafter executing the provided python code:\n\n```python\na = 24\nm = 11**2\nmod_inverse(a, m)\n```\n\nthe answer is found to be: 116.\n\nthe answer is correct.",
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"is_correct": true,
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"trial": -1
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}
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