Use Stokes' Theorem to evaluate

Double integrate (grad XF).dSwhereFis (z, exp(xyz), -x) and surface S is that part of the sphere x^2+(y-2)^2+z^2=10 for y=>1 with the normal pointing outwards.

I know I need to use IntegrateF.dSas an equivalent, but how do I parameterise the equation and get the domain?