I thought it's a straightforward exercise on the divergence theorem, yet it looks like [itex]\operatorname{div} f = 0 [/itex]. So the surface integral is zero?

Am I missing some sort of a trick here? The exercise isn't supposed to be that easy.

true, ##\operatorname{div} f = 0## but what is the surface? Is it a closed surface or not closed and do they give some specific surface to integrate over?

ah, right, ##S^2## means sphere. I forgot about that. hmm, yeah it looks like zero is the right answer then. well, don't look a gift horse in the mouth :)