requests
ability
failure (to operate)
offers
permission
necessity
guesses
suggestions / advice
expectations
Could / Would / Can somebody turn the lights off, please?
There should / ought to be a handout going around.
I should / ought to / have to / need to / 'd better stop ('d = had)
The projector won't connect to my laptop.
The projector must be warming up. it might / could / may be broken.
Can you all see the screen?
I'll make the screen bigger. I can / could turn it up.
May* / Could / Can I ask a question? Yes, you may* / can. (*More formal)
You might want to check out the articles on the handout.