SkillCompiler/data/format-preference/natural-instructions/tasks/task090_equation_learner_algebra.json

{
    "Contributors": [
        "Neeraj Varshney"
    ],
    "Source": [
        "synthetic"
    ],
    "URL": [
        NaN
    ],
    "Categories": [
        "Mathematics"
    ],
    "Reasoning": [
        "Numerical Reasoning",
        "Quantitative Reasoning",
        "Mathematics -> Algebra"
    ],
    "Definition": [
        "A ploynomial equation is a sum of terms. Here each term is either a constant number, or consists of the variable x raised to a certain power and multiplied by a number. These numbers are called weights. For example, in the polynomial: 2x^2+3x+4, the weights are: 2,3,4. You can present a polynomial with the list of its weights, for example, equation weights = [6, 4] represent the equation 6x + 4 and equation weights = [1, 3, 4] represent the equation 1x^2 + 3x + 4. In this task, you need to compute the result of a polynomial expression by substituing a given value of x in the given polynomial equation. Equation weights are given as a list."
    ],
    "Input_language": [
        "English"
    ],
    "Output_language": [
        "English"
    ],
    "Instruction_language": [
        "English"
    ],
    "Domains": [
        "Mathematics"
    ],
    "Positive Examples": [
        {
            "input": "x = 3, equation weights = [4, 2]",
            "output": "14",
            "explanation": "Here, the weights represent the polynomial: 4x + 2, so we should multiply 4 by 3, and add it to 2 which results in (4*3 + 2 =) 14."
        },
        {
            "input": "x = 2, equation weights = [3, 2, 4]",
            "output": "20",
            "explanation": "Here, the weights represent the polynomial: 3x^2 + 2x + 4. To find the result, we should substitute 2 for x to get: 3*(2)^2 + 2*2 + 4, which equals 20."
        }
    ],
    "Negative Examples": [
        {
            "input": "x = 4, equation weights = [5, 1]",
            "output": "19",
            "explanation": "Here, the answer should have been 21 as 5*4 + 1 = 21 instead of 19."
        },
        {
            "input": "x=5, equation weights = [1,3]",
            "output": "16",
            "explanation": "Pay attention to the order of the weights. Here, if we mistakenly create the polynomial as 3x + 1, we will find the result as 16, but the correct way to create the polynomial is: 1x + 3, which results in 8."
        }
    ],
    "Instances": [
        {
            "id": "task090-1551104d504742e081808134cf471645",
            "input": "x = 9, equation weights = [5, 2]",
            "output": [
                "47"
            ]
        },
        {
            "id": "task090-17f18dc486a34d98a32d109924522b39",
            "input": "x = 9, equation weights = [5, 0]",
            "output": [
                "45"
            ]
        },
        {
            "id": "task090-5b709225ffdf4362aeb4c0b43918365b",
            "input": "x = 5, equation weights = [9, 2, 5]",
            "output": [
                "240"
            ]
        },
        {
            "id": "task090-2c9640ab64f5496abd96b117efce08ed",
            "input": "x = 1, equation weights = [6, 2, 4, 7]",
            "output": [
                "19"
            ]
        },
        {
            "id": "task090-54d9e3581dc144d286a8ef536b2b6784",
            "input": "x = 1, equation weights = [5, 9, 1]",
            "output": [
                "15"
            ]
        },
        {
            "id": "task090-4a35c6100db34dca88f03200a4205a27",
            "input": "x = 3, equation weights = [2, 3, 9]",
            "output": [
                "36"
            ]
        },
        {
            "id": "task090-2b294d78b8184ce3b1ac5aab82244a0c",
            "input": "x = 5, equation weights = [4, 5]",
            "output": [
                "25"
            ]
        },
        {
            "id": "task090-facb95f9e335459198c37721fbd1a145",
            "input": "x = 4, equation weights = [1, 2, 7]",
            "output": [
                "31"
            ]
        },
        {
            "id": "task090-1ac417f27b124861984650f1ad954e8a",
            "input": "x = 7, equation weights = [0, 5]",
            "output": [
                "5"
            ]
        },
        {
            "id": "task090-e064e550412c4266b5f3219140a970cb",
            "input": "x = 9, equation weights = [5, 1]",
            "output": [
                "46"
            ]
        },
        {
            "id": "task090-affbd717fb7f470f84375521738e2b32",
            "input": "x = 4, equation weights = [9, 5]",
            "output": [
                "41"
            ]
        },
        {
            "id": "task090-d3ed4866204742bcbf61af2f2f6f61c2",
            "input": "x = 9, equation weights = [3, 7, 8, 6, 2]",
            "output": [
                "25490"
            ]
        },
        {
            "id": "task090-0851945bceee4e37b8924e9b417c5283",
            "input": "x = 10, equation weights = [2, 7, 1, 4, 3]",
            "output": [
                "27143"
            ]
        },
        {
            "id": "task090-b027ff6120434cfcb01bc7233789321f",
            "input": "x = 2, equation weights = [2, 6, 1]",
            "output": [
                "21"
            ]
        },
        {
            "id": "task090-a87e0c0eeba54201ae249f9ca15b0c9b",
            "input": "x = 9, equation weights = [4, 2]",
            "output": [
                "38"
            ]
        },
        {
            "id": "task090-4b61c585724c4e4abcbd11c297b39408",
            "input": "x = 7, equation weights = [1, 4]",
            "output": [
                "11"
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            "input": "x = 0, equation weights = [9, 7]",
            "output": [
                "7"
            ]
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            "id": "task090-d325a61713c647a29573b518cb2c73d2",
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            "output": [
                "37"
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                "4"
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            "output": [
                "13"
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            "output": [
                "1673"
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            "output": [
                "49"
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            "id": "task090-24c2109a7678496793b363f95d819f0c",
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                "1122"
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            "output": [
                "40"
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            "input": "x = 8, equation weights = [7, 8]",
            "output": [
                "64"
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            "output": [
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            "output": [
                "24"
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            "output": [
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            "output": [
                "31"
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            "id": "task090-cf66b0a6d3004498a4c0798bf0d0ed84",
            "input": "x = 3, equation weights = [8, 4]",
            "output": [
                "28"
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