>>11637041I'm not even American, but my vector calculus professor would often just write the integrals on the board and say something like "if you do the calculations you will se that the answer is this (writes down the answer) but this is an advanced course, so you should be able to do the calculations yourself. If you've doubts meet me on my office hours".
I don't even know he bothered doing numerical examples, since he would only rarely actually do any of the work, and often skip all steps (at most commenting on a useful change of variables)