task090_equation_learner_algebra.json

{
    "Contributors": [
        "Neeraj Varshney"
    ],
    "Source": [
        "Synthetic"
    ],
    "Categories": [
        "Answer Geneartion",
        "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.",
    "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": [
        {
            "input": "x = 9, equation weights = [5, 2]",
            "output": [
                "47"
            ]
        },
        {
            "input": "x = 9, equation weights = [5, 0]",
            "output": [
                "45"
            ]
        },
        {
            "input": "x = 5, equation weights = [9, 2, 5]",
            "output": [
                "240"
            ]
        },
        {
            "input": "x = 1, equation weights = [6, 2, 4, 7]",
            "output": [
                "19"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 9, 1]",
            "output": [
                "15"
            ]
        },
        {
            "input": "x = 3, equation weights = [2, 3, 9]",
            "output": [
                "36"
            ]
        },
        {
            "input": "x = 5, equation weights = [4, 5]",
            "output": [
                "25"
            ]
        },
        {
            "input": "x = 4, equation weights = [1, 2, 7]",
            "output": [
                "31"
            ]
        },
        {
            "input": "x = 7, equation weights = [0, 5]",
            "output": [
                "5"
            ]
        },
        {
            "input": "x = 9, equation weights = [5, 1]",
            "output": [
                "46"
            ]
        },
        {
            "input": "x = 4, equation weights = [9, 5]",
            "output": [
                "41"
            ]
        },
        {
            "input": "x = 9, equation weights = [3, 7, 8, 6, 2]",
            "output": [
                "25490"
            ]
        },
        {
            "input": "x = 10, equation weights = [2, 7, 1, 4, 3]",
            "output": [
                "27143"
            ]
        },
        {
            "input": "x = 2, equation weights = [2, 6, 1]",
            "output": [
                "21"
            ]
        },
        {
            "input": "x = 9, equation weights = [4, 2]",
            "output": [
                "38"
            ]
        },
        {
            "input": "x = 7, equation weights = [1, 4]",
            "output": [
                "11"
            ]
        },
        {
            "input": "x = 0, equation weights = [9, 7]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 4, equation weights = [8, 5]",
            "output": [
                "37"
            ]
        },
        {
            "input": "x = 10, equation weights = [0, 4]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 1, equation weights = [6, 7]",
            "output": [
                "13"
            ]
        },
        {
            "input": "x = 4, equation weights = [6, 0, 7, 4, 9]",
            "output": [
                "1673"
            ]
        },
        {
            "input": "x = 2, equation weights = [7, 8, 5]",
            "output": [
                "49"
            ]
        },
        {
            "input": "x = 9, equation weights = [8, 3, 0]",
            "output": [
                "675"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 4, 1]",
            "output": [
                "10"
            ]
        },
        {
            "input": "x = 7, equation weights = [1, 3]",
            "output": [
                "10"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 4, 3, 7]",
            "output": [
                "1122"
            ]
        },
        {
            "input": "x = 9, equation weights = [8, 2]",
            "output": [
                "74"
            ]
        },
        {
            "input": "x = 9, equation weights = [1, 2]",
            "output": [
                "11"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 0]",
            "output": [
                "40"
            ]
        },
        {
            "input": "x = 8, equation weights = [7, 8]",
            "output": [
                "64"
            ]
        },
        {
            "input": "x = 10, equation weights = [6, 1, 2]",
            "output": [
                "612"
            ]
        },
        {
            "input": "x = 8, equation weights = [3, 0]",
            "output": [
                "24"
            ]
        },
        {
            "input": "x = 9, equation weights = [7, 1, 6]",
            "output": [
                "582"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 7, 3]",
            "output": [
                "238"
            ]
        },
        {
            "input": "x = 8, equation weights = [3, 7]",
            "output": [
                "31"
            ]
        },
        {
            "input": "x = 3, equation weights = [8, 4]",
            "output": [
                "28"
            ]
        },
        {
            "input": "x = 7, equation weights = [7, 3, 5]",
            "output": [
                "369"
            ]
        },
        {
            "input": "x = 1, equation weights = [8, 9, 4]",
            "output": [
                "21"
            ]
        },
        {
            "input": "x = 1, equation weights = [0, 5]",
            "output": [
                "5"
            ]
        },
        {
            "input": "x = 0, equation weights = [1, 0, 3, 7]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 10, equation weights = [1, 9]",
            "output": [
                "19"
            ]
        },
        {
            "input": "x = 6, equation weights = [8, 3, 5]",
            "output": [
                "311"
            ]
        },
        {
            "input": "x = 8, equation weights = [5, 8, 1, 6, 3]",
            "output": [
                "24691"
            ]
        },
        {
            "input": "x = 3, equation weights = [0, 4, 6]",
            "output": [
                "18"
            ]
        },
        {
            "input": "x = 4, equation weights = [6, 1, 3, 5]",
            "output": [
                "417"
            ]
        },
        {
            "input": "x = 3, equation weights = [4, 5, 3, 0, 2]",
            "output": [
                "488"
            ]
        },
        {
            "input": "x = 0, equation weights = [1, 6, 0]",
            "output": [
                "0"
            ]
        },
        {
            "input": "x = 5, equation weights = [1, 2]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 3, equation weights = [3, 0, 9]",
            "output": [
                "36"
            ]
        },
        {
            "input": "x = 8, equation weights = [9, 5]",
            "output": [
                "77"
            ]
        },
        {
            "input": "x = 6, equation weights = [5, 1, 2]",
            "output": [
                "188"
            ]
        },
        {
            "input": "x = 7, equation weights = [4, 7]",
            "output": [
                "35"
            ]
        },
        {
            "input": "x = 4, equation weights = [5, 4]",
            "output": [
                "24"
            ]
        },
        {
            "input": "x = 9, equation weights = [3, 1, 4]",
            "output": [
                "256"
            ]
        },
        {
            "input": "x = 8, equation weights = [3, 8]",
            "output": [
                "32"
            ]
        },
        {
            "input": "x = 4, equation weights = [0, 1, 7, 3]",
            "output": [
                "47"
            ]
        },
        {
            "input": "x = 2, equation weights = [8, 5]",
            "output": [
                "21"
            ]
        },
        {
            "input": "x = 2, equation weights = [6, 1]",
            "output": [
                "13"
            ]
        },
        {
            "input": "x = 1, equation weights = [2, 8, 9]",
            "output": [
                "19"
            ]
        },
        {
            "input": "x = 4, equation weights = [0, 7]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 8, equation weights = [5, 9, 2]",
            "output": [
                "394"
            ]
        },
        {
            "input": "x = 2, equation weights = [1, 2]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 7, equation weights = [1, 6, 2]",
            "output": [
                "93"
            ]
        },
        {
            "input": "x = 2, equation weights = [7, 8, 3]",
            "output": [
                "47"
            ]
        },
        {
            "input": "x = 4, equation weights = [3, 7, 2]",
            "output": [
                "78"
            ]
        },
        {
            "input": "x = 9, equation weights = [7, 5]",
            "output": [
                "68"
            ]
        },
        {
            "input": "x = 3, equation weights = [8, 1, 6]",
            "output": [
                "81"
            ]
        },
        {
            "input": "x = 2, equation weights = [7, 9, 1]",
            "output": [
                "47"
            ]
        },
        {
            "input": "x = 3, equation weights = [9, 3]",
            "output": [
                "30"
            ]
        },
        {
            "input": "x = 1, equation weights = [2, 3, 5]",
            "output": [
                "10"
            ]
        },
        {
            "input": "x = 9, equation weights = [4, 5]",
            "output": [
                "41"
            ]
        },
        {
            "input": "x = 5, equation weights = [7, 5]",
            "output": [
                "40"
            ]
        },
        {
            "input": "x = 6, equation weights = [5, 7, 4]",
            "output": [
                "226"
            ]
        },
        {
            "input": "x = 0, equation weights = [0, 2, 9]",
            "output": [
                "9"
            ]
        },
        {
            "input": "x = 1, equation weights = [9, 2, 1]",
            "output": [
                "12"
            ]
        },
        {
            "input": "x = 9, equation weights = [3, 8, 1]",
            "output": [
                "316"
            ]
        },
        {
            "input": "x = 4, equation weights = [2, 3]",
            "output": [
                "11"
            ]
        },
        {
            "input": "x = 6, equation weights = [2, 5, 8]",
            "output": [
                "110"
            ]
        },
        {
            "input": "x = 0, equation weights = [6, 8, 1]",
            "output": [
                "1"
            ]
        },
        {
            "input": "x = 1, equation weights = [6, 0]",
            "output": [
                "6"
            ]
        },
        {
            "input": "x = 0, equation weights = [2, 5]",
            "output": [
                "5"
            ]
        },
        {
            "input": "x = 5, equation weights = [9, 6]",
            "output": [
                "51"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 4]",
            "output": [
                "44"
            ]
        },
        {
            "input": "x = 0, equation weights = [6, 4, 1]",
            "output": [
                "1"
            ]
        },
        {
            "input": "x = 7, equation weights = [8, 3, 5]",
            "output": [
                "418"
            ]
        },
        {
            "input": "x = 10, equation weights = [8, 2, 5]",
            "output": [
                "825"
            ]
        },
        {
            "input": "x = 0, equation weights = [7, 0]",
            "output": [
                "0"
            ]
        },
        {
            "input": "x = 10, equation weights = [6, 7]",
            "output": [
                "67"
            ]
        },
        {
            "input": "x = 1, equation weights = [1, 4, 3]",
            "output": [
                "8"
            ]
        },
        {
            "input": "x = 7, equation weights = [7, 6, 8]",
            "output": [
                "393"
            ]
        },
        {
            "input": "x = 3, equation weights = [3, 1]",
            "output": [
                "10"
            ]
        },
        {
            "input": "x = 0, equation weights = [5, 4, 0]",
            "output": [
                "0"
            ]
        },
        {
            "input": "x = 10, equation weights = [4, 1, 9, 5, 2]",
            "output": [
                "41952"
            ]
        },
        {
            "input": "x = 0, equation weights = [9, 8, 2]",
            "output": [
                "2"
            ]
        },
        {
            "input": "x = 5, equation weights = [7, 3]",
            "output": [
                "38"
            ]
        },
        {
            "input": "x = 10, equation weights = [4, 1, 2, 7, 6]",
            "output": [
                "41276"
            ]
        },
        {
            "input": "x = 8, equation weights = [4, 1, 3]",
            "output": [
                "267"
            ]
        },
        {
            "input": "x = 7, equation weights = [5, 4, 8, 6]",
            "output": [
                "1973"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 6, 7]",
            "output": [
                "237"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 6, 9]",
            "output": [
                "20"
            ]
        },
        {
            "input": "x = 2, equation weights = [8, 7]",
            "output": [
                "23"
            ]
        },
        {
            "input": "x = 0, equation weights = [3, 6]",
            "output": [
                "6"
            ]
        },
        {
            "input": "x = 1, equation weights = [0, 4, 3, 2, 9]",
            "output": [
                "18"
            ]
        },
        {
            "input": "x = 8, equation weights = [0, 4]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 0, equation weights = [6, 7]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 6, equation weights = [4, 8, 9]",
            "output": [
                "201"
            ]
        },
        {
            "input": "x = 8, equation weights = [8, 5, 4]",
            "output": [
                "556"
            ]
        },
        {
            "input": "x = 10, equation weights = [6, 4, 7, 1]",
            "output": [
                "6471"
            ]
        },
        {
            "input": "x = 2, equation weights = [3, 5, 4]",
            "output": [
                "26"
            ]
        },
        {
            "input": "x = 10, equation weights = [5, 4]",
            "output": [
                "54"
            ]
        },
        {
            "input": "x = 0, equation weights = [5, 2, 1]",
            "output": [
                "1"
            ]
        },
        {
            "input": "x = 9, equation weights = [1, 0]",
            "output": [
                "9"
            ]
        },
        {
            "input": "x = 8, equation weights = [9, 8]",
            "output": [
                "80"
            ]
        },
        {
            "input": "x = 10, equation weights = [5, 1, 7]",
            "output": [
                "517"
            ]
        },
        {
            "input": "x = 6, equation weights = [2, 1, 3]",
            "output": [
                "81"
            ]
        },
        {
            "input": "x = 3, equation weights = [1, 7, 2]",
            "output": [
                "32"
            ]
        },
        {
            "input": "x = 1, equation weights = [3, 1]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 5, equation weights = [6, 1, 2]",
            "output": [
                "157"
            ]
        },
        {
            "input": "x = 4, equation weights = [0, 3, 4]",
            "output": [
                "16"
            ]
        },
        {
            "input": "x = 5, equation weights = [8, 4, 2]",
            "output": [
                "222"
            ]
        },
        {
            "input": "x = 0, equation weights = [2, 6, 7]",
            "output": [
                "7"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 1]",
            "output": [
                "6"
            ]
        },
        {
            "input": "x = 1, equation weights = [6, 8, 2, 5, 3]",
            "output": [
                "24"
            ]
        },
        {
            "input": "x = 7, equation weights = [9, 2, 8]",
            "output": [
                "463"
            ]
        },
        {
            "input": "x = 0, equation weights = [2, 6]",
            "output": [
                "6"
            ]
        },
        {
            "input": "x = 3, equation weights = [1, 9]",
            "output": [
                "12"
            ]
        },
        {
            "input": "x = 9, equation weights = [0, 5]",
            "output": [
                "5"
            ]
        },
        {
            "input": "x = 10, equation weights = [3, 5, 2, 0]",
            "output": [
                "3520"
            ]
        },
        {
            "input": "x = 1, equation weights = [6, 3, 9]",
            "output": [
                "18"
            ]
        },
        {
            "input": "x = 6, equation weights = [8, 9]",
            "output": [
                "57"
            ]
        },
        {
            "input": "x = 5, equation weights = [0, 4, 6]",
            "output": [
                "26"
            ]
        },
        {
            "input": "x = 6, equation weights = [1, 3]",
            "output": [
                "9"
            ]
        },
        {
            "input": "x = 4, equation weights = [8, 2, 5]",
            "output": [
                "141"
            ]
        },
        {
            "input": "x = 4, equation weights = [8, 2, 9]",
            "output": [
                "145"
            ]
        },
        {
            "input": "x = 10, equation weights = [0, 2]",
            "output": [
                "2"
            ]
        },
        {
            "input": "x = 5, equation weights = [2, 3]",
            "output": [
                "13"
            ]
        },
        {
            "input": "x = 10, equation weights = [1, 5, 2]",
            "output": [
                "152"
            ]
        },
        {
            "input": "x = 4, equation weights = [3, 5]",
            "output": [
                "17"
            ]
        },
        {
            "input": "x = 8, equation weights = [3, 6]",
            "output": [
                "30"
            ]
        },
        {
            "input": "x = 9, equation weights = [2, 7]",
            "output": [
                "25"
            ]
        },
        {
            "input": "x = 4, equation weights = [9, 3]",
            "output": [
                "39"
            ]
        },
        {
            "input": "x = 8, equation weights = [8, 9]",
            "output": [
                "73"
            ]
        },
        {
            "input": "x = 4, equation weights = [9, 6]",
            "output": [
                "42"
            ]
        },
        {
            "input": "x = 2, equation weights = [9, 1, 8]",
            "output": [
                "46"
            ]
        },
        {
            "input": "x = 2, equation weights = [2, 3, 5]",
            "output": [
                "19"
            ]
        },
        {
            "input": "x = 3, equation weights = [0, 6]",
            "output": [
                "6"
            ]
        },
        {
            "input": "x = 10, equation weights = [7, 8, 3, 9, 6]",
            "output": [
                "78396"
            ]
        },
        {
            "input": "x = 6, equation weights = [6, 8]",
            "output": [
                "44"
            ]
        },
        {
            "input": "x = 0, equation weights = [6, 2, 5, 0, 4]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 1, equation weights = [7, 0, 3, 5]",
            "output": [
                "15"
            ]
        },
        {
            "input": "x = 5, equation weights = [6, 3]",
            "output": [
                "33"
            ]
        },
        {
            "input": "x = 10, equation weights = [4, 2, 9]",
            "output": [
                "429"
            ]
        },
        {
            "input": "x = 4, equation weights = [0, 8, 2]",
            "output": [
                "34"
            ]
        },
        {
            "input": "x = 9, equation weights = [4, 0, 8]",
            "output": [
                "332"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 7, 0]",
            "output": [
                "12"
            ]
        },
        {
            "input": "x = 3, equation weights = [8, 0, 1]",
            "output": [
                "73"
            ]
        },
        {
            "input": "x = 5, equation weights = [4, 3, 6]",
            "output": [
                "121"
            ]
        },
        {
            "input": "x = 1, equation weights = [0, 2, 9]",
            "output": [
                "11"
            ]
        },
        {
            "input": "x = 4, equation weights = [0, 7, 2]",
            "output": [
                "30"
            ]
        },
        {
            "input": "x = 3, equation weights = [5, 9, 8, 0]",
            "output": [
                "240"
            ]
        },
        {
            "input": "x = 5, equation weights = [3, 6, 8, 9, 0]",
            "output": [
                "2870"
            ]
        },
        {
            "input": "x = 1, equation weights = [5, 9, 4]",
            "output": [
                "18"
            ]
        },
        {
            "input": "x = 9, equation weights = [0, 4]",
            "output": [
                "4"
            ]
        },
        {
            "input": "x = 0, equation weights = [4, 1]",
            "output": [
                "1"
            ]
        },
        {
            "input": "x = 3, equation weights = [8, 1, 7, 2, 3]",
            "output": [
                "747"
            ]
        },
        {
            "input": "x = 4, equation weights = [7, 9, 5]",
            "output": [
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}