$$\int_0^1 a^k x^k d x=$$

Let $$\alpha$$ and $$\beta(\alpha<\beta)$$ are roots of $$18 x^2-9 \pi x+\pi^2=0, f(x)=x^2, g(x)=\cos x$$. Then, $$\int_\alpha^\beta x(g \circ f(x)) d x=$$

$$\int_0^\pi x\left(\sin ^2(\sin x)+\cos ^2(\cos x)\right) d x=$$

If $$\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}} $$, then the value of a is equal to