Evaluate the following definite integrals:

(a) $\int_0^1 x^2e^x dx =$ .

(b) $\int_0^1 x^2 2^x dx =$ .

(c) $\int_1^2 (\ln(x))^2 dx =$ .

(d) $\int_0^{\frac \pi 2} \cos^{6}(x) dx =$ .