I think I may have just answered my own question. I think I've been reading over everything too quickly and not paying attention to the difference between flux and net flux.
Either way, some clarification could be nice. Would a flat disc still be considered a closed surface, with a net flux of...
I understand that magnetic flux through a closed surface is zero, but what is the exact definition of a closed surface? The textbook I'm using is rather vague with this definition and I want to make sure I have the definition nailed down for the exam in case my professor tries anything tricky.