prompt list | ground_truth string |
|---|---|
[
{
"content": "Evaluate the integral: \\[ \\int_{0}^{\\sqrt[6]{\\pi}} x^5 \\cos(x^6) \\, dx \\]",
"role": "user"
}
] | 0 |
[
{
"content": "True or False: If $B = \\{b_1, \\dots, b_n\\}$ is a basis for $\\mathbb{R}^n$ and for every $1 \\le i \\le n$, there exists a vector $v_i$ such that $Av_i = b_i$, then the matrix $A$ is invertible.",
"role": "user"
}
] | A |
[
{
"content": "Find the value of $X$ that satisfies the equation involving recursive $n$-th roots:\n\\[ \\sqrt[n]{X+\\sqrt[n]{X+\\sqrt[n]{X+ \\dots}}} =\\sqrt[n]{X\\sqrt[n]{X\\sqrt[n]{X \\dots}}} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $281,242.74 |
[
{
"content": "Can the maximum capacity cut in a network be determined in O(m) time complexity using the residual graph obtained after finding the maximum flow?",
"role": "user"
}
] | No |
[
{
"content": "Find the highest lower bound for the probability of getting exactly one head when tossing $d$ pairwise independent coins, each with a probability of $1/d$ of landing heads.",
"role": "user"
}
] | \dfrac{1}{d} |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for any real number \\( x \\), the following equalities hold: \\( f(x+1) = 1 + f(x) \\) and \\( f(x^4 - x^2) = f^4(x) - f^2(x) \\).",
"role": "user"
}
] | f(x) = x |
[
{
"content": "Calculate the limit: $$\\lim_{h\\rightarrow0}\\sup_{n\\in\\mathbb{N}}\\left\\|\\sqrt{n}\\,\\mathbb{1}_{(0,\\frac{1}{n})}(x+h)-\\sqrt{n}\\,\\mathbb{1}_{(0,\\frac{1}{n})}(x)\\right\\|_{L^2(\\mathbb{R})}$$",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Given the function \\( F(x) = \\int_0^{2x} \\tan(t^2) \\, dt \\), find \\( F''(1) \\).",
"role": "user"
}
] | 16 \sec^2(4) |
[
{
"content": "Determine the value of \\(a\\) such that the inequality \\(\\log \\frac{1}{\\div}\\left(\\sqrt{x^{2}+a x+5}+1\\right) \\cdot \\log _{5}\\left(x^{2}+a x+6\\right)+\\log _{a} 3 \\geqslant 0\\) has exactly one solution.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the integral \\( \\iint_{T_a} (x+y) \\, dx \\, dy \\) using the change of variables \\( u = x+y \\) and \\( v = x \\), where \\( T_a \\) is the region in the \\( xy \\) plane bounded by the \\( x \\) and \\( y \\) axes and the line \\( x+y = a \\).",
"role": "user"
}
] | \dfrac{a^3}{3} |
[
{
"content": "Consider a geodesically convex Riemannian manifold $M$, where for any two points $p, q \\in M$, there is a unique minimizing geodesic connecting them. For a point $p \\in M$, is the function $f(x) = (d(x, p))^2$ smooth, where $d$ is the distance function on $M$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the group to which \\((\\mathbb{Z}\\times\\mathbb{Z})/\\langle (1,2) \\rangle\\) is isomorphic.",
"role": "user"
}
] | \mathbb{Z} |
[
{
"content": "Determine the largest integer $n$ such that $13^n$ divides the product of all factorials from $1!$ to $26!$. Provide your answer as a single integer.",
"role": "user"
}
] | 15 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | r=a |
[
{
"content": "Determine which is larger: $23^{120}$ or $49^{96}$.",
"role": "user"
}
] | 23^{120} |
[
{
"content": "A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\\displaystyle\n{{a\\pi+b\\sqrt{c}}\\over{d\\pi-e\\sqrt{f}}}$, where $a$, $b$,... | 592 |
[
{
"content": "Anakin's age and the ages of his three children are all prime numbers, and their combined ages sum to 50. After n years, the sum of the children's ages will be twice Anakin's age. Given that Anakin's age is a prime number, and the ages of his three children form a unique set of primes, determine t... | 43 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2526.089 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.056 mol |
[
{
"content": "An encoder maps source codewords $x \\in \\{0,1\\}^K$ to channel codewords $y \\in \\{0,1\\}^{N'}$ with $K/N' < 1$. The corresponding decoder maps a codeword $r \\in \\{0,1\\}^{N'}$ to a source codeword $\\hat{x} \\in \\{0,1\\}^K$. Assume this coding scheme can correctly decode codewords at the ou... | q |
[
{
"content": "Determine the set of invertible elements in the quadratic integer ring $A=\\Bbb Z[\\sqrt{-5}]$, denoted as $U(A)$. Provide your answer as a set.",
"role": "user"
}
] | \{1, -1\} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 68.4 N |
[
{
"content": "Given the joint density function for two random variables \\(X\\) and \\(Y\\): \\[ f(x,y) = \\frac{e^{-\\frac{x}{y}} e^{-y}}{y} \\] where \\(x, y \\in (0, \\infty)^2\\), find the conditional expectation \\(E(X|Y=y)\\) for all \\(y > 0\\).",
"role": "user"
}
] | y |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19 years |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | sodium borohydride |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.153738 C |
[
{
"content": "Find the sum of all positive integers \\( n \\) such that \\( \\frac{n+7}{25n+7} \\) is the square of a rational number.",
"role": "user"
}
] | 21 |
[
{
"content": "The equation $x^2-4x+7=19$ has two solutions, $a$ and $b$, with $a\\geq b$. What is the value of $2a+b$?",
"role": "user"
}
] | 10 |
[
{
"content": "Does the set of continuous functions with compact support, $C_c(X)$, separate points in a separable, infinite-dimensional Banach space $X$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.39e-29 C.m |
[
{
"content": "Evaluate the line integral \\( \\int_{C} Pdx + Qdy \\) where \\( P(x,y) = \\frac{y}{x^2+y^2} \\) and \\( Q(x,y) = \\frac{-x}{x^2+y^2} \\), and \\( C \\) is a piecewise smooth Jordan curve in the set \\( S = \\{(x,y) | x^2 +y^2 >0 \\} \\) that encloses the origin.",
"role": "user"
}
] | -2\pi |
[
{
"content": "Determine whether the function \\( \\varphi(x) = \\int_2^x \\frac{1}{\\log(t)}e^{-\\frac{1}{\\sqrt{t}}}~dt \\) is an asymptotic lower bound for the prime counting function \\( \\pi(x) \\).",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7560 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19.6 N |
[
{
"content": "Determine the number of rotations in \\(\\mathbb{R}^3\\) that preserve the cube \\(C = [-1,1]^3\\).",
"role": "user"
}
] | 24 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.25 percent |
[
{
"content": "Is it possible to traverse a 4x4x4 cube, starting at one corner and moving to adjacent 1x1x1 cubes, to reach the cube diagonally opposite the starting corner? Model this problem as a bipartite graph and determine the possibility of such a traversal.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $781.25 |
[
{
"content": "Determine whether the following statement is true or false: If $f_k$, $k=1,2,\n\\dots, n$ are linearly dependent continuous functions on $(-1,1)$, then the functions $\\int_0^x f_k(t)\\,dt$, $k=1,2,\\dots, n$ are also linearly dependent on $(-1,1)$. Provide a justification for your answer.",
"... | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | federal constitutional republic |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | q1 = 5.00 nC, q2 = 20.00 nC |
[
{
"content": "Tangents are drawn from the point \\((-2\\sqrt{3}, 2)\\) to the hyperbola \\(y^2 - x^2 = 4\\). The chord of contact of these tangents subtends an angle \\(\\theta\\) at the center of the hyperbola. Calculate the value of \\(12 \\tan^2 \\theta\\).",
"role": "user"
}
] | 9 |
[
{
"content": "Let $V = \\mathbb{R}^3$ be an inner product space with the standard dot product. Suppose $v$ is a unit vector in $V$. Determine the number of orthogonal operators $T: V \\to V$ such that $T((1,0,0)) = v$. \\( \\boxed{} \\)",
"role": "user"
}
] | \infty |
[
{
"content": "Let \\( K \\) be a field and consider \\( a \\in K \\) with \\( f(x) = x^n - a \\) being an irreducible polynomial. If \\( m \\in \\mathbb{N} \\) is a divisor of \\( n \\), and \\( \\alpha \\) is a root of \\( f(x) \\) in an extension field of \\( K \\), determine the minimal polynomial of \\( \\a... | x^{n/m} - a |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 194 units |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.55 s |
[
{
"content": "$r(x)$ has domain $\\{-1,0,1,2\\}$ and range $\\{0,2,4,6\\}$. $s(x)$ has domain $\\{1,2,3,4\\}$ and is defined by $s(x)=x+1$. What is the sum of all possible values of $s(r(x))$?",
"role": "user"
}
] | 8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | E0 |
[
{
"content": "Determine the minimum dimension n such that the system of differential equations \\( x' = Ax \\) is satisfied, where \\( A \\) is an \\( n \\times n \\) matrix and the first coordinate of the solution \\( x(t) \\) is given by \\( x_1(t) = 5t^2\\cos(3t) + 2\\sin(3t) - e^{2t}\\sin(3t) + 4t \\). What... | 10 |
[
{
"content": "Determine whether Grandi's Sum, given by the series \\(1 - 1 + 1 - 1 + 1 - 1 + \\ldots + (-1)^n + \\ldots\\), is equal to \\(\\frac{1}{2}\\).",
"role": "user"
}
] | \frac{1}{2} |
[
{
"content": "Let $A$ be a real symmetric positive semi-definite matrix. If $v^TAv = 0$ for $v \\in \\mathbb{R}^n$, does it imply that $Av = 0$? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.84 trillion rupees |
[
{
"content": "Consider a $(0,1)$-matrix $A$ with $m$ rows and $m^2$ columns, where each column contains exactly three $1$'s. What is the minimum number of rows that need to be removed to ensure that no column has more than two $1$'s?",
"role": "user"
}
] | m - 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $23.899 billion |
[
{
"content": "Compute the value of the probability generating function \\( f(x) = \\left(\\frac{x(x^7 - 1)}{7(x - 1)}\\right)^7 \\) at \\( x = 21 \\).",
"role": "user"
}
] | 270163281^7 |
[
{
"content": "Let $f(x)$ be a real-valued twice differentiable function on the interval $[1, 5]$ such that $f(1) = f(5) = 0$ and $f(x) = f'(x) + f''(x)$ for all $x \\in [1, 5]$. Find the value of $f(2) + f(4) - f'(3)$. \\( \\text{Express your answer as a single number.} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the radius of convergence for the function \\( \\frac{1}{z^2 + 2z + 2} \\).",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 40.40 m |
[
{
"content": "Does there exist a sequence \\( \\{A_n\\} \\) of subsets in \\( B(H) \\) that satisfies the DS property, where \\( H \\) is a separable Hilbert space?",
"role": "user"
}
] | Yes |
[
{
"content": "A parabola and an ellipse share a focus, and the directrix of the parabola is the line containing the minor axis of the ellipse. The parabola and ellipse intersect at two points. Given that the equation of the ellipse is $\\frac{x^2}{25} + \\frac{y^2}{9} = 1,$ find the distance between those two p... | \tfrac{4\sqrt{14}}{3} |
[
{
"content": "Determine the values of the parameter \\( a \\) such that the matrices \\( A = \\begin{pmatrix} 1 & 4-a-a^2 \\\\ 2 & -1 \\end{pmatrix} \\) and \\( B = \\begin{pmatrix} -a-1 & 3 \\\\ 3 & -5 \\end{pmatrix} \\) represent the same bilinear form in different bases.",
"role": "user"
}
] | -2 |
[
{
"content": "Determine the side length of the square base of a square pyramid with equilateral triangular faces that can completely contain a cuboid with dimensions 25 (height) x 50 (width) x 50 (length), given that the bottom of the cuboid is 26 units above the base of the pyramid.",
"role": "user"
}
] | 50 + 51\sqrt{2} |
[
{
"content": "A fair six-sided die is rolled repeatedly. What is the expected number of rolls needed to get two consecutive sixes?",
"role": "user"
}
] | 42 |
[
{
"content": "Determine the number of nonabelian groups of order 2009.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the value of $k$ such that the determinant of the matrix \\[\\begin{vmatrix}(b+c)^2 & a^2 & a^2 \\\\ b^2 & (c+a)^2 & b^2 \\\\ c^2 & c^2 & (a+b)^2\\end{vmatrix}\\] equals $k(abc)(a+b+c)^3$. Provide your answer as a single integer or fraction.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -0.8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | atleast {eq}1.1\times 10^{-28} M{/eq} but not equal or greater than {eq}6.3\times 10^{-26} M{/eq} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19N |
[
{
"content": "How many circles of radius \\(\\frac{\\pi}{4}\\) can be drawn within a circle of radius \\(\\pi\\) such that they do not intersect one another?",
"role": "user"
}
] | 19 |
[
{
"content": "In a von Neumann algebra, if $A_{\\alpha}$ converges to $0$ in the $\\sigma$-weak topology, do the positive parts $(A_{\\alpha})_{+}$ necessarily converge to $0$ in the $\\sigma$-weak topology?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 415 N |
[
{
"content": "Given two non-zero $p$-dimensional column vectors $a$ and $b$, determine the possible number of distinct eigenvalues for the matrix $M = ab^t + ba^t$. Choose the correct option:\n\n(a) 1\n(b) 2\n(c) 1 or 2\n(d) 1 or 2 or 3",
"role": "user"
}
] | D |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.84 x 10^-9 g/mL |
[
{
"content": "Compute the limit \\( \\lim_{x\\to 0}\\frac{e^{3x}-e^{-3x}}{\\Gamma(x)^{-1}} \\) using the fact that the residue of \\( \\Gamma \\) at \\( z=0 \\) is 1.",
"role": "user"
}
] | 6 |
[
{
"content": "Determine the kernel of the linear map $F_A: \\mathbb{R}^{n \\times n} \\rightarrow \\mathbb{R}^{n \\times n}$ defined by $F_A(B) = AB^T$, where $A$ is an orthogonal $n \\times n$ matrix.",
"role": "user"
}
] | \{0\} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 676N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.45 g |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty} \\oint_{\\partial S_n} \\frac{f(w)}{w-z}\\, dw \\) for a fixed \\( z\\in\\mathbb{C} \\) that is not a pole of \\( f \\), where \\( S_n \\) is the square centered at \\( n + \\frac{1}{2} \\) with side length 1 in the complex plane, and \\( f(z) = \\frac{1... | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.897 J/gC |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Class 6 |
[
{
"content": "Determine whether the statement is true: If $(b) \\subset (c) \\subset R$, with $b \\neq 0$, then $(c)/(b) \\simeq R/(b:c)$, where $a \\cdot c = b$.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | K = (10 / 18^9)^(1/10), L = (180)^(1/10) |
[
{
"content": "Given that \\( xf(x) - yf(y) = (x-y)f(x+y) \\) for a differentiable function \\( f \\) defined on \\( \\mathbb{R} \\), find the value of \\( f'(2x) \\). Choose from the following options: \\( f'(x), 2f'(x), xf'(x), 4f'(x), \\) or \\( 8f'(x) \\).",
"role": "user"
}
] | f'(x) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 25.5 |
[
{
"content": "Determine whether the following statement is true or false: If \\( \\frac{a^2 + c^2}{b^2+d^2} = \\left(\\frac{a+c}{b+d}\\right)^2 \\), does it necessarily follow that \\( \\frac{a}{b} = \\frac{c}{d} \\)?",
"role": "user"
}
] | B |
[
{
"content": "Calculate the average distance between two points on the circumference of a circle with radius 1.",
"role": "user"
}
] | \dfrac{4}{\pi} |
[
{
"content": "Let $\\Omega$ be a convex subset of $\\mathbb{R}^N$ with a smooth boundary. Consider the space $M = \\{f : \\Omega \\to \\mathbb{R} \\mid \\lvert|f\\rvert|_{W^{1,N+1}} \\in \\mathbb{R}^+\\} \\setminus I$, where $I$ is the set of all functions that have at least one isolated discontinuity. Consider... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The overstatement of income before tax for each of the five quarters are $741 million, $535.75 million, $652.75 million, $766.75 million, and $597.25 million, respectively. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | [Ar]3d^5 4s^1 |
[
{
"content": "Find the limit: $$\\lim_{x\\to\\infty} \\frac{ 1}{x \\sqrt{x} } \\int_{0}^{x} \\ln \\frac{t^{3} + 2}{t^{2} +1 } dt $$",
"role": "user"
}
] | 0 |
[
{
"content": "At a party, each man danced with exactly three women and each woman danced with exactly two men. Twelve men attended the party. How many women attended the party?",
"role": "user"
}
] | 18 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 193.57 N |
[
{
"content": "The sequence \\(\\{\\alpha_{n}\\}\\) is an arithmetic sequence with common difference \\(\\beta\\). The sequence \\(\\{\\sin \\alpha_{n}\\}\\) is a geometric sequence with common ratio \\(q\\). Given that \\(\\alpha_{1}\\) and \\(\\beta\\) are real numbers, determine the value of \\(q\\).",
"r... | \pm 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | - 18266.398 Pa |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $28,416 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | When the price is less than or equal to 500: q = 0; When the price is greater than 500: p = 50q + 500 |
[
{
"content": "What is the remainder when $333^{333}$ is divided by $11$?",
"role": "user"
}
] | 5 |
[
{
"content": "Find the value of $P(1)$ for the polynomial $P(x)$ that satisfies the equation $P(P(x)+1) = 9P(x) + 8$. Provide your answer as a single number.",
"role": "user"
}
] | 8 |
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