I am having difficulty setting up this problem. I know the bounds must be 0 to pi/2 for both theta and phi but I am unsure as to how to calculate the integrand. I know it must be the double integral of F*ds, but I do not know how to get F or ds. If anyone can help me set up the integral or give steps to follow so I can solve the problem I would greatly appreciate it.
So after a lot of help from Bye_World I was able to come up with the correct answer:
$\int_0^{2\pi} \int_0^{\pi /2} \left[576\sin^2(\phi) \sin(\theta)+4096\sin^3(\phi) \cos^2(\theta) \cos(\phi)\right] d\theta d\phi$ which equals to $1024\pi$.