27. “We do not normally use modal verbs to say
that situations definitely exist or that
particular events definitely happened. We
use them, for example, to talk about things
which we expect, which are not possible,
which we think are necessary, which we
want to happen, which we are not sure
about, which tend to happen, or which have
not happened.”
Michael Swan
Practical English Usage
OUP
30. indicative modal
I have to get up early tomorrow. I must get up early tomorrow.
[be able to] Can you play the piano?
Perhaps it isn’t a good idea. [may]
[be important] You mustn’t smoke.
Do you want me to carry your bags? [shall]
[be able to] I couldn’t do the exercise.
Please give us permission to go now. [may]
[be going to] It will rain this evening.
It was possible to see the hills. [could]
[want] They’d like to have a party.
31. indicative modal
I have to get up early tomorrow. I must get up early tomorrow.
Are you able to play the piano? Can you play the piano?
Perhaps it isn’t a good idea. It may not be a good idea.
It’s important that you don’t smoke. You mustn’t smoke.
Do you want me to carry your bags? Shall I carry your bags?
I wasn’t able to do the exercise. I couldn’t do the exercise.
Please give us permission to go now. May we go now?
It’s going to rain this evening. It will rain this evening.
It was possible to see the hills. We could see the hills.
They want to have a party. They’d like to have a party.