data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of $0.\\overline{6}$ and $0.\\overline{7}$ as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{9}"
} | {
"index": 5800,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of $213_4 + 132_4 + 321_4$ and express your answer in base $4$."
}
] | math | {
"style": "rule",
"ground_truth": "1332_4"
} | {
"index": 5801,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of $2367 + 3672 + 6723 + 7236$."
}
] | math | {
"style": "rule",
"ground_truth": "19998"
} | {
"index": 5802,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of $5.46$, $2.793$, and $3.1$ as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "11.353"
} | {
"index": 5803,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of $5.47 + 4.96$ and express it as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "10.43"
} | {
"index": 5804,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of 5739204.742 and -176817.835, and round the result to the nearest integer."
}
] | math | {
"style": "rule",
"ground_truth": "5562387"
} | {
"index": 5805,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of all four-digit numbers that can be formed using the digits 0, 1, 2, 3, and 4, with no repeated digits."
}
] | math | {
"style": "rule",
"ground_truth": "259980"
} | {
"index": 5806,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of all integers between 50 and 450 that end in 1 or 7."
}
] | math | {
"style": "rule",
"ground_truth": "19920"
} | {
"index": 5807,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of all integers greater than 4 and less than 21."
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 5808,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of eight occurrences of the term $5^5$:\n\\[ 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 \\]\nA) $5^6$\nB) $5^7$\nC) $5^8$\nD) $5^{6.29248125}$\nE) $40^5$"
}
] | math | {
"style": "rule",
"ground_truth": "5^{6.29248125}"
} | {
"index": 5809,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the $2023$ roots of $(x-1)^{2023} + 2(x-2)^{2022} + 3(x-3)^{2021} + \\cdots + 2022(x-2022)^2 + 2023(x-2023)$."
}
] | math | {
"style": "rule",
"ground_truth": "2021"
} | {
"index": 5810,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the coefficients of $P(x)$ if $\\left(20 x^{27}+2 x^{2}+1\\right) P(x)=2001 x^{2001}$."
}
] | math | {
"style": "rule",
"ground_truth": "87"
} | {
"index": 5811,
"solution": "The sum of coefficients of $f(x)$ is the value of $f(1)$ for any polynomial $f$. Plugging in 1 to the above equation, $P(1)=\\frac{2001}{23}=87$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the distances from one vertex of a rectangle with length 3 and width 4 to the midpoints of each of its sides.\nA) $6 + \\sqrt{5}$ \nB) $7 + \\sqrt{12}$ \nC) $7.77 + \\sqrt{13}$ \nD) $9 + \\sqrt{15}$"
}
] | math | {
"style": "rule",
"ground_truth": "7.77 + \\sqrt{13}"
} | {
"index": 5812,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the distances from one vertex of a rectangle with sides of lengths $3$ and $5$ to the midpoints of each of the sides of the rectangle.\nA) $11.2$\nB) $12.4$\nC) $13.1$\nD) $14.5$\nE) $15.2$"
}
] | math | {
"style": "rule",
"ground_truth": "13.1"
} | {
"index": 5813,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the first 4 terms of the geometric sequence $\\{a_n\\}$."
}
] | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 5814,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the first five prime numbers that have a units digit of 3."
}
] | math | {
"style": "rule",
"ground_truth": "135"
} | {
"index": 5815,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the first six terms of the geometric series $3 + \\left(\\frac{1}{3}\\right) + \\left(\\frac{1}{3}\\right)^2 + \\left(\\frac{1}{3}\\right)^3 + \\left(\\frac{1}{3}\\right)^4 + \\left(\\frac{1}{3}\\right)^5$. Express your answer as a simplified fraction."
}... | math | {
"style": "rule",
"ground_truth": "\\frac{364}{81}"
} | {
"index": 5816,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the following fractions: $\\frac{1}{12} + \\frac{2}{12} + \\frac{3}{12} + \\frac{4}{12} + \\frac{5}{12} + \\frac{6}{12} + \\frac{7}{12} + \\frac{8}{12} + \\frac{9}{12} + \\frac{65}{12} + \\frac{3}{4}$.\nA) $\\frac{119}{12}$\nB) $9$\nC) $\\frac{113}{12}$\nD)... | math | {
"style": "rule",
"ground_truth": "\\frac{119}{12}"
} | {
"index": 5817,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the geometric series $1+\\left(\\frac{1}{3}\\right)+\\left(\\frac{1}{3}\\right)^2 + \\left(\\frac{1}{3}\\right)^3 + \\dots$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"index": 5818,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the geometric series $1+\\left(\\frac{1}{5}\\right)+\\left(\\frac{1}{5}\\right)^2 + \\left(\\frac{1}{5}\\right)^3 + \\dots$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{4}"
} | {
"index": 5819,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the geometric series $3 - \\left(\\frac{3}{4}\\right) + \\left(\\frac{3}{4}\\right)^2 - \\left(\\frac{3}{4}\\right)^3 + \\dots$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{7}"
} | {
"index": 5820,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the integers 122 and 78, express both numbers and the resulting sum in base-5."
}
] | math | {
"style": "rule",
"ground_truth": "1300_5"
} | {
"index": 5821,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the repeating decimals $0.\\overline{2}$, $0.\\overline{02}$, and $0.\\overline{0002}$ as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{224422}{9999}"
} | {
"index": 5822,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the sequence $2 - 6 + 10 - 14 + 18 - \\cdots - 98 + 102$."
}
] | math | {
"style": "rule",
"ground_truth": "-52"
} | {
"index": 5823,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the series $(3+13+23+33+43)+(11+21+31+41+51)$."
}
] | math | {
"style": "rule",
"ground_truth": "270"
} | {
"index": 5824,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the series $1-2-3+4+5-6-7+8+9-10-11+\\cdots+1998+1999-2000-2001$."
}
] | math | {
"style": "rule",
"ground_truth": "2001"
} | {
"index": 5825,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the series $\\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{n^{5}}$ with an accuracy of $10^{-3}$."
}
] | math | {
"style": "rule",
"ground_truth": "0.973"
} | {
"index": 5826,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the series:\n\\[\n\\sum_{n=1}^\\infty \\frac{3^n}{1 + 3^n + 3^{n+1} + 3^{2n+1}}.\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 5827,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the square of the binomial coefficients: $C_2^2+C_3^2+C_4^2+…+C_{11}^2$."
}
] | math | {
"style": "rule",
"ground_truth": "220"
} | {
"index": 5828,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum of the squares of the roots of the equation \\[x\\sqrt{x} - 8x + 9\\sqrt{x} - 3 = 0,\\] given that all roots are real and nonnegative."
}
] | math | {
"style": "rule",
"ground_truth": "46"
} | {
"index": 5829,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum:\n\\[\n\\sum_{n=1}^\\infty \\frac{n^3 + n^2 + n - 1}{(n+3)!}\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 5830,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum:\n\\[\\sum_{N = 1}^{2048} \\lfloor \\log_3 N \\rfloor.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "12049"
} | {
"index": 5831,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum: \n\\[\n\\left(\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{2016}\\right)+\\left(\\frac{2}{3}+\\frac{2}{4}+\\cdots+\\frac{2}{2016}\\right)+\\left(\\frac{3}{4}+\\frac{3}{5}+\\cdots+\\frac{3}{2016}\\right)+\\cdots+\\left(\\frac{2014}{2015}+\\frac{2014}{2016}\\rig... | math | {
"style": "rule",
"ground_truth": "1015560"
} | {
"index": 5832,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum: $\\dfrac{2}{100} + \\dfrac{5}{1000} + \\dfrac{8}{10000} + \\dfrac{6}{100000}$."
}
] | math | {
"style": "rule",
"ground_truth": "0.02586"
} | {
"index": 5833,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum: $\\sum_{n=1}^{99} \\left(n^{3}+3n^{2}+3n\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "25502400"
} | {
"index": 5834,
"solution": "The sum is calculated as follows: $$\\begin{aligned} & \\left(1^{3}+3 \\cdot 1^{2}+3 \\cdot 1\\right)+\\left(2^{3}+3 \\cdot 2^{2}+3 \\cdot 2\\right)+\\cdots+\\left(99^{3}+3 \\cdot 99^{2}+3 \\cdot 99\\right) \\\\ & =\\left(1^{3}+3 \\cdot 1^{2}+3 \\cdot 1+1\\right)+\\left(2^{3}+3 \\cdot ... |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the surface area of the part of the paraboloid of revolution \\( 3y = x^2 + z^2 \\) that is located in the first octant and bounded by the plane \\( y = 6 \\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{39 \\pi}{4}"
} | {
"index": 5835,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the surface integrals of the first kind:\na) \\(\\iint_{\\sigma}|x| dS\\), where \\(\\sigma\\) is defined by \\(x^2 + y^2 + z^2 = 1\\), \\(z \\geqslant 0\\).\n\nb) \\(\\iint_{\\sigma} (x^2 + y^2) dS\\), where \\(\\sigma\\) is defined by \\(x^2 + y^2 = 2z\\), \\(z = 1\... | math | {
"style": "rule",
"ground_truth": "3\\sqrt{2} \\pi"
} | {
"index": 5836,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the total area of a pentagon with sides of lengths 18, 25, 30, 28, and 25 units, assuming it can be divided into a right triangle and a trapezoid."
}
] | math | {
"style": "rule",
"ground_truth": "995"
} | {
"index": 5837,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the total surface area of two hemispheres of radius 8 cm each, joined at their bases to form a complete sphere. Assume that one hemisphere is made of a reflective material that doubles the effective surface area for purposes of calculation. Express your answer in term... | math | {
"style": "rule",
"ground_truth": "384\\pi"
} | {
"index": 5838,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value for the expression $\\sqrt{25\\sqrt{15\\sqrt{9}}}$."
}
] | math | {
"style": "rule",
"ground_truth": "5\\sqrt{15}"
} | {
"index": 5839,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of\n$$\n\\sqrt{2018 \\times 2021 \\times 2022 \\times 2023 + 2024^{2}} - 2024^{2}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "-12138"
} | {
"index": 5840,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of \n\\[\\left(\\left(\\left((3+2)^{-1}+1\\right)^{-1}+2\\right)^{-1}+1\\right)^{-1}+1.\\]\nA) $\\frac{40}{23}$\nB) $\\frac{17}{23}$\nC) $\\frac{23}{17}$\nD) $\\frac{23}{40}$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{40}{23}"
} | {
"index": 5841,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $$1+\\cfrac{2}{3+\\cfrac{6}{7}}$$ and express it as a simplified fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{41}{27}"
} | {
"index": 5842,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $(-3 \\frac{3}{8})^{- \\frac{2}{3}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{9}"
} | {
"index": 5843,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $(2345 + 3452 + 4523 + 5234) \\times 2$."
}
] | math | {
"style": "rule",
"ground_truth": "31108"
} | {
"index": 5844,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $(3,1) \\nabla (4,2)$ using the operation ' $\\nabla$ ' defined by $(a, b) \\nabla (c, d)=ac+bd$."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5845,
"solution": "From the definition, $(3,1) \\nabla (4,2)=(3)(4)+(1)(2)=12+2=14$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $({-\\frac{4}{5}})^{2022} \\times ({\\frac{5}{4}})^{2021}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"index": 5846,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $1.000 + 0.101 + 0.011 + 0.001$."
}
] | math | {
"style": "rule",
"ground_truth": "1.113"
} | {
"index": 5847,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $1357 + 3571 + 5713 - 7135$."
}
] | math | {
"style": "rule",
"ground_truth": "3506"
} | {
"index": 5848,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $15 \\times 30 + 45 \\times 15$."
}
] | math | {
"style": "rule",
"ground_truth": "1125"
} | {
"index": 5849,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $333 + 33 + 3$."
}
] | math | {
"style": "rule",
"ground_truth": "369"
} | {
"index": 5850,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $3^{12} \\cdot 3^3$ and express it as some integer raised to the third power."
}
] | math | {
"style": "rule",
"ground_truth": "243"
} | {
"index": 5851,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $8\\cos ^{2}25^{\\circ}-\\tan 40^{\\circ}-4$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"index": 5852,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $V_3$ for the polynomial $f(x) = 2x^6 + 5x^5 + 6x^4 + 23x^3 - 8x^2 + 10x - 3$ at $x = -4$ using the Horner's method."
}
] | math | {
"style": "rule",
"ground_truth": "-49"
} | {
"index": 5853,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $V_3$ in Horner's method (also known as Qin Jiushao algorithm) for finding the value of the polynomial $f(x) = 4x^6 + 3x^5 + 4x^4 + 2x^3 + 5x^2 - 7x + 9$ when $x = 4$."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 5854,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\cos 96^\\circ \\cos 24^\\circ - \\sin 96^\\circ \\sin 66^\\circ$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"index": 5855,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\cos \\frac{\\pi}{7} \\cos \\frac{2\\pi}{7} \\cos \\frac{4\\pi}{7} = \\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{8}"
} | {
"index": 5856,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\dfrac{\\sqrt[3]{81}}{\\sqrt[4]{81}}$ in terms of 81 raised to what power?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{12}"
} | {
"index": 5857,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\displaystyle\\frac{245^2-225^2}{20}$."
}
] | math | {
"style": "rule",
"ground_truth": "470"
} | {
"index": 5858,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\frac12\\cdot\\frac41\\cdot\\frac18\\cdot\\frac{16}{1} \\dotsm \\frac{1}{2048}\\cdot\\frac{4096}{1}$, and multiply the result by $\\frac34$."
}
] | math | {
"style": "rule",
"ground_truth": "1536"
} | {
"index": 5859,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\frac{17!}{7!10!}$."
}
] | math | {
"style": "rule",
"ground_truth": "408408"
} | {
"index": 5860,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\frac{1}{2 + \\frac{1}{3 + \\frac{1}{4}}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{30}"
} | {
"index": 5861,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\frac{2 \\times 3 + 4}{2 + 3}$."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5862,
"solution": "Evaluating, $\\frac{2 \\times 3+4}{2+3}=\\frac{6+4}{5}=\\frac{10}{5}=2$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\frac{2468_{10}}{111_{3}} - 3471_{9} + 1234_{7}$. Express your answer in base 10."
}
] | math | {
"style": "rule",
"ground_truth": "-1919"
} | {
"index": 5863,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\left(\\left((4-1)^{-1} - 1\\right)^{-1} - 1\\right)^{-1} - 1$."
}
] | math | {
"style": "rule",
"ground_truth": "$\\frac{-7}{5}$"
} | {
"index": 5864,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\left(\\sum_{k=1}^{10} \\log_{4^k} 2^{k^2}\\right)\\cdot\\left(\\sum_{k=1}^{50} \\log_{16^k} 64^k\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "2062.5"
} | {
"index": 5865,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\log_{2}9 \\cdot \\log_{3}5 \\cdot \\log_{\\sqrt{5}}8 = \\_\\_\\_\\_\\_\\_.$"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5866,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\sin 135^{\\circ}\\cos (-15^{\\circ}) + \\cos 225^{\\circ}\\sin 15^{\\circ}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 5867,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\sin 68^{\\circ} \\sin 67^{\\circ} - \\sin 23^{\\circ} \\cos 68^{\\circ}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"index": 5868,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\sqrt{\\frac{\\sqrt{81} + \\sqrt{81}}{2}}$."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 5869,
"solution": "Calculating, $\\sqrt{\\frac{\\sqrt{81} + \\sqrt{81}}{2}} = \\sqrt{\\frac{9 + 9}{2}} = \\sqrt{9} = 3$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $\\text{rem} \\left(\\frac{5}{7}, \\frac{3}{4}\\right)$ and then multiply the result by $-2$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{10}{7}"
} | {
"index": 5870,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $n$ such that\n\\[(1 + \\tan 1^\\circ)(1 + \\tan 2^\\circ)(1 + \\tan 3^\\circ) \\dotsm (1 + \\tan 30^\\circ) = 2^n.\\]"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 5871,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $v_2$ when $x = 2$ for $f(x) = 3x^4 + x^3 + 2x^2 + x + 4$ using Horner's method."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5872,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $v_4$ for the polynomial $f(x) = 12 + 35x - 8x^2 + 79x^3 + 6x^4 + 5x^5 + 3x^6$ using the Horner's method when $x = -4$."
}
] | math | {
"style": "rule",
"ground_truth": "220"
} | {
"index": 5873,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of $x$ when the arithmetic mean of the following five expressions is 30: $$x + 10 \\hspace{.5cm} 3x - 5 \\hspace{.5cm} 2x \\hspace{.5cm} 18 \\hspace{.5cm} 2x + 6$$"
}
] | math | {
"style": "rule",
"ground_truth": "15.125"
} | {
"index": 5874,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of \\(\\sin \\left(-\\frac{5 \\pi}{3}\\right) + \\cos \\left(-\\frac{5 \\pi}{4}\\right) + \\tan \\left(-\\frac{11 \\pi}{6}\\right) + \\cot \\left(-\\frac{4 \\pi}{3}\\right)\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3} - \\sqrt{2}}{2}"
} | {
"index": 5875,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of \\[\\cot(\\cot^{-1}5 + \\cot^{-1}11 + \\cot^{-1}17 + \\cot^{-1}23).\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{97}{40}"
} | {
"index": 5876,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression\n\n$$\n\\frac{\\left(3^{4}+4\\right) \\cdot\\left(7^{4}+4\\right) \\cdot\\left(11^{4}+4\\right) \\cdot \\ldots \\cdot\\left(2015^{4}+4\\right) \\cdot\\left(2019^{4}+4\\right)}{\\left(1^{4}+4\\right) \\cdot\\left(5^{4}+4\\right) \\cdot\\left... | math | {
"style": "rule",
"ground_truth": "4080401"
} | {
"index": 5877,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression $(8 \\times 6)-(4 \\div 2)$."
}
] | math | {
"style": "rule",
"ground_truth": "46"
} | {
"index": 5878,
"solution": "We evaluate the expression by first evaluating the expressions in brackets: $(8 \\times 6)-(4 \\div 2)=48-2=46$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression $2 \\times 0 + 2 \\times 4$."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 5879,
"solution": "Calculating, $2 \\times 0 + 2 \\times 4 = 0 + 8 = 8$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression $2+3 \times 5+2$."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 5880,
"solution": "Calculating, $2+3 \times 5+2=2+15+2=19$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression $\\frac{1+(3 \\times 5)}{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 5881,
"solution": "Using the correct order of operations, $\\frac{1+(3 \\times 5)}{2}=\\frac{1+15}{2}=\\frac{16}{2}=8$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression $\\left(2 \\times \\frac{1}{3}\\right) \\times \\left(3 \\times \\frac{1}{2}\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 5882,
"solution": "Re-arranging the order of the numbers being multiplied, $\\left(2 \\times \\frac{1}{3}\\right) \\times \\left(3 \\times \\frac{1}{2}\\right) = 2 \\times \\frac{1}{2} \\times 3 \\times \\frac{1}{3} = \\left(2 \\times \\frac{1}{2}\\right) \\times \\left(3 \\times \\frac{1}{3}\\right) = 1... |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression \\( \\sqrt{\\frac{16^{12} + 8^{15}}{16^5 + 8^{16}}} \\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\sqrt{2}}{4}"
} | {
"index": 5883,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression \\(\\sin \\frac{b \\pi}{36}\\), where \\(b\\) is the sum of all distinct numbers obtained from the number \\(a = 987654321\\) by cyclic permutations of its digits (in a cyclic permutation, all the digits of the number, except the last one, ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"index": 5884,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression \\[(5^{1003}+6^{1004})^2-(5^{1003}-6^{1004})^2\\] and express it in the form of $k\\cdot30^{1003}$ for some positive integer $k$."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 5885,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression given by: $$2 + \\cfrac{3}{4 + \\cfrac{5}{6}}.$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{76}{29}"
} | {
"index": 5886,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the expression: $3 - 7 + 11 - 15 + 19 - \\cdots - 59 + 63 - 67 + 71$."
}
] | math | {
"style": "rule",
"ground_truth": "-36"
} | {
"index": 5887,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the following expression and find angle $\\theta$ if the number can be expressed as $r e^{i \\theta}$, where $0 \\le \\theta < 2\\pi$:\n\\[ e^{11\\pi i/60} + e^{21\\pi i/60} + e^{31 \\pi i/60} + e^{41\\pi i /60} + e^{51 \\pi i /60} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{31\\pi}{60}"
} | {
"index": 5888,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the following expressions:\n\n1. $\\sqrt[4]{(3-\\pi )^{4}}+(0.008)\\;^{- \\frac {1}{3}}-(0.25)\\;^{ \\frac {1}{2}}×( \\frac {1}{ \\sqrt {2}})^{-4}$\n2. $\\log _{3} \\sqrt {27}-\\log _{3} \\sqrt {3}-\\lg 625-\\lg 4+\\ln (e^{2})- \\frac {4}{3}\\lg \\sqrt {8... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5889,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the following expressions: \n(1) $$\\sqrt[4]{(3-\\pi )^{4}}$$ + (0.008) $$^{- \\frac {1}{3}}$$ - (0.25) $$^{ \\frac {1}{2}}$$ × ($$\\frac {1}{ \\sqrt {2}}$$)$$^{-4}$$; \n(2) $\\log_{3}$$\\sqrt {27}$$ - $\\log_{3}$$\\sqrt {3}$$ - $\\lg{625}$ - $\\lg{4}$ ... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5890,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the following expressions: \n(1) $(2 \\frac {7}{9})^{0.5}+0.1^{-2}+(2 \\frac {10}{27})^{- \\frac {2}{3}}-3\\pi^{0}+ \\frac {37}{48}$; \n(2) $(-3 \\frac {3}{8})^{- \\frac {2}{3}}+(0.002)^{- \\frac {1}{2}}-10(\\sqrt {5}-2)^{-1}+(\\sqrt {2}- \\sqrt {3})^{0... | math | {
"style": "rule",
"ground_truth": "- \\frac {167}{9}"
} | {
"index": 5891,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the following product as a common fraction:\n\\[ \\left(2 \\cdot \\left(1-\\frac{1}{2}\\right)\\right) \\cdot \\left(1-\\frac{1}{3}\\right) \\cdot \\left(1-\\frac{1}{4}\\right) \\dotsm \\left(1-\\frac{1}{50}\\right) \\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{50}"
} | {
"index": 5892,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the function $f(x)=3x^{6}-2x^{5}+x^{3}+1$ at $x=2$ using the Horner's method (also known as the Qin Jiushao algorithm) to determine the value of $v_{4}$."
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"index": 5893,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the polynomial $f(x) = 3x^6 + 4x^5 + 5x^4 + 6x^3 + 7x^2 + 8x + 1$ at $x=0.4$ using Horner's method, and then determine the value of $v_1$."
}
] | math | {
"style": "rule",
"ground_truth": "5.2"
} | {
"index": 5894,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the value of the polynomial f(x) = 7x^7 + 6x^6 + 5x^5 + 4x^4 + 3x^3 + 2x^2 + x using the Qin Jiushao algorithm when x = 3. Find the value of V₄."
}
] | math | {
"style": "rule",
"ground_truth": "789"
} | {
"index": 5895,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the values of:\n(1) $8^{\\frac{2}{3}} - (0.5)^{-3} + \\left(\\frac{1}{\\sqrt{3}}\\right)^{-2} \\times \\left(\\frac{81}{16}\\right)^{-\\frac{1}{4}}$;\n(2) $\\log 5 \\cdot \\log 8000 + (\\log 2^{\\sqrt{3}})^2 + e^{\\ln 1} + \\ln(e \\sqrt{e})$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{11}{2}"
} | {
"index": 5896,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume in cubic centimeters of a truncated cone formed by cutting a smaller cone from a larger cone. The larger cone has a diameter of 8 cm at the base and a height of 10 cm. The smaller cone, which is cut from the top, has a diameter of 4 cm and a height of 4 cm.... | math | {
"style": "rule",
"ground_truth": "48\\pi"
} | {
"index": 5897,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of a tetrahedron with vertices at points $A_{1}, A_{2}, A_{3}, A_{4}$, and its height dropped from vertex $A_{4}$ to the face $A_{1} A_{2} A_{3}$.\n\n$A_{1}(-2, 0, -4)$\n\n$A_{2}(-1, 7, 1)$\n\n$A_{3}(4, -8, -4)$\n\n$A_{4}(1, -4, 6)$"
}
] | math | {
"style": "rule",
"ground_truth": "5\\sqrt{2}"
} | {
"index": 5898,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the volume of an octahedron which has an inscribed sphere of radius 1."
}
] | math | {
"style": "rule",
"ground_truth": "4\\sqrt{3}"
} | {
"index": 5899,
"solution": ""
} |
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