Please note that this is not a homework question. Simply a question that if you change the value of the force in your surface integral in this case, shouldn't the answer be different?
Why is it that when the force field is z^2 and you take the surface integral over a sphere of radius a using spherical coordinates, that yields the flux to be (4pi a^3 )/ 3
BUT in a calculus book, the force field is z instead of z^2 evaluated using polar coordinates and it yields the same...