Polite question, would you, could you, will you, can you

(a) Would you please open the door? Yes
(b) Could you please open the door? Yes. Of course
(c) Will you please open the door? Certainly. I'd be happy to
(d) Can you please open the door? Of course. I’d be glad to.
Sure. (Informal)
Okay. (Informal)
Uh-huh. (Meaning “yes”)
I’m sorry. I’d like to help, but my hands are full.
People use would you, could you, will you, and can you to ask polite questions. The questions ask for someone’s help or cooperation. (a), (b), (c) and (d) have basically the same meaning. The use of can, as in (d), is less formal than the others.
Note: may is not used when you is the subject of a polite question.
Incorrect: may you please open the door?