Be able to

Be able to has similar meaning to can and could.

He is able to support her. (= He can support her.)
She is able to speak ten languages. (= She can speak ten languages.)
They were able to catch the thief. (= They could catch the thief.)
Be to

The structure be + to indicates simple future, like will or shall, but with a slight degree of uncertainty.

He is to retire this year.
We are to go on a vacation next month.
Be + to can also be used to express commands. This structure has  similar meaning to must, but not quiet so strong or blunt.

You are to leave at once. (= You must leave at once.)
He is to report for duty within a week. (= He must report for duty within a week.)

Had better

Had better has similar meaning to should and ought.

You had better consult a doctor. (= You should consult a doctor.)
You had better get some rest. (= You ought to get some rest.)

Had better may also express a threat.

You had better give me my money back.
He had better be careful.
Have to and have got to

I have to be there by 12 o’clock. (= I must be there by 12 o’clock.)

Fill in the blanks with suitable modal auxiliary verbs.

1. Pay your fees in time lest you —————- be fined.

a) would
b) should
c) will

2.————- I send an application?

a) will
b) shall
c) may

3. ————– he be allowed to play the match?

a) shall
b) will
c) must

4. If I were you, I ————- do it.

a) wouldn’t
b) shouldn’t
c) must not

Answers

1. should
2. shall
3. will
4. wouldn’t