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[{"content":"Compute the definite integral:\n\n$$\n\\int_{\\pi / 2}^{\\pi} 2^{4} \\cdot \\sin ^{6} x(...TRUNCATED)

[" Alright, so I have this integral to compute: the integral from π/2 to π of 2^4 times sin^6 x ti(...TRUNCATED)

[{"content":"Alex, a mid-career attorney, is considering opening a solo practice. Currently, Alex ea(...TRUNCATED)

[" Okay, let's see. So, Alex wants to start a solo practice and make sure that in the first year, th(...TRUNCATED)

[{"content":"As shown in the figure, point $D$ is an interior point of $\\triangle ABC$. $BD$ inters(...TRUNCATED)

[" Okay, so I need to find the measure of angle BFC in triangle ABC where point D is inside the tria(...TRUNCATED)

[{"content":"A car rental company owns 100 cars. When the monthly rental fee per car is 3000 Yuan, a(...TRUNCATED)

[" Okay, let me see. I need to figure out the monthly rental fee per car that maximizes the revenue (...TRUNCATED)

[{"content":"Given an isosceles triangle \\(ABC\\) where \\(AB = AC\\) and \\(\\angle ABC = 53^\\cir(...TRUNCATED)

[" Okay, so I have this problem about an isosceles triangle ABC where AB equals AC, and angle ABC is(...TRUNCATED)

[{"content":"Let $ABCD$ be a parallelogram such that $\\angle BAD = 60^{\\circ}.$ Let $K$ and (...TRUNCATED)

[" Okay, so I have this geometry problem here: Let ABCD be a parallelogram with angle BAD = 60 degre(...TRUNCATED)

[{"content":"Cat Matroskin, Uncle Fyodor, postman Pechkin, and Sharik sat at a round table. Each had(...TRUNCATED)

[" Okay, let me try to figure out this problem step by step. So we have four people sitting around a(...TRUNCATED)

[{"content":"Mrs. Thompson is a worried mother who is trying to support her child, Alex, who is inte(...TRUNCATED)

[" Okay, let me try to figure this out step by step. So, Mrs. Thompson wants to read a 240-page book(...TRUNCATED)

[{"content":"Triangle $ABC$, $ADE$, and $EFG$ are all equilateral. Points $D$ and $G$ are midpoints (...TRUNCATED)

[" Okay, so I need to find the perimeter of the figure ABCDEFG. The problem states that triangles AB(...TRUNCATED)

[{"content":"As a political scholar focused on international relations and geopolitical analysis, yo(...TRUNCATED)

[" Alright, let me try to tackle this problem step by step. So, the user is a political scholar deal(...TRUNCATED)