I couldn't find an online example worked out, surprisingly.
Most of the stuff in the wiki article isn't needed for your case. What you need is the expression for the force on a current carrying wire: F = I (L X B). F is the force, I is the current. L is a vector with magnitude equal to the length of the wire, and its direction is the direction of the current flow. B is the magnetic field vector. All of this assumes a constant field along the wire and a straight wire.
That's likely not the case, so you have to go to infinitesimal wire segements and integrate: dF = I (dL x B).
I don't know if this has made it any clearer for you, I'm assuming from your post history that you have done stuff with vectors/numerical integration before and just needed the bullpucky separated from the stuff you need in the wiki article. If it hasn't helped, I wouldn't mind doing an example in Perl tonight/tomorrow evening if nobody else has.
Edit: How is your model of the situation stored? I assume you've got a function that, given x,y,z, gives you the magnetic field vector at that point, but what of the wire?