Modeling physical systems is already hard. I don't think we could yet write down the dynamics of the physical systems well enough (or rather, we don't understand what the most important characteristics are) to come up with a precise formulation of the major problems in synthetic biology or nanotechnology. I certainly concede that an optimizer would be helpful in solving many subproblems, and would considerably increase the speed of new developments in pretty much every field. I don't think it solves many problems on its own though.

But even if you could solve narrow existing technological problems or develop new technologies at a steady pace, it seems like you should be able to do more. Suppose the box can do in a minute what takes existing humans a million years. Then our only upper bound on our capabilities using the box is whatever we expect of a million years of progress at the current pace. I don't know about you, but I expect pretty much everything.