I am tempted to attack some bits of the responses you have gotten so far! Instead I will tell you that I believe the answer is very simple.
- Put yourself in the professors shoes. (I have to assume you have the ability to do that, even if it requires great effort.)
- Now, do what you would want a student to do if the tables were turned.
As simple (and as old hat) as this sounds, it is a cure for many ills that is far too rarely practiced.
(Another relevant fact: scientists - mathematicians included - almost always take themselves and what they do far too seriously!)