Need help evaluating integral (stoke's theorem)?

To evaluate the surface integral as a closed line integral (Stoke's Theorem), you need to first find the boundary of the surface, ie. the three 1/4 circcle arcs in the xy, yz and zx planes and break the line integral into 3 parts and integrate each. But IMO, it's probably just easier to just do the surface integral directly. Line integrals are not necessarily any easier and you have to do 3 in this case, although they're probably identical because of the symmetry in F and you can avoid the del "cross".