After I, you can use should instead of would.
The very first thing I should do would be to teach you how to cook.
I should be very unhappy on the continent.
belief: must and cannot
5.123 You use must to show that you believe something is the case, because of particular facts or circumstances.
Oh, you must be Sylvia’s husband.
Fashion must account for a small percentage of sales.
This article must have been written by a woman.
When you are indicating that something is not the case, you use cannot. You do not use must not. (See paragraph 5.126.)
The two conflicting messages cannot possibly both be true.
You can’t have forgotten me.
He can’t have said that. He just can’t.
present possibility: could, might, and may
5.124 You use could, might, or may to say that there is a possibility of something happening or being the case. May is slightly more formal than could or might; otherwise there is very little difference in meaning between these modals.
Don’t eat it. It could be poisonous.
His route from the bus stop might be the same as yours.
In rare cases the jaw may be broken during extraction.
If you put well after could, might, or may, you are saying that it is fairly likely that something is the case.
It could well be that the economic situation is getting better.
His predictions could well have come true.
You might well be right.
I think that may well have been the intention.
negative possibility: might not and may not
5.125 You use might not or may not to say that it is possible that something is not the case.
He might not be in England at all.
That mightn’t be true.
That may not sound very imposing.
impossibility: could not and cannot
5.126 You use could not or cannot to say that it is impossible that something is the case.
…knowledge which could not have been gained in any other way.
It couldn’t possibly be poison.
He cannot know everything that is going on.
You can’t talk to the dead.
strong assertion: could not with comparatives
5.127 Could is sometimes used in negative constructions with the comparative form of an adjective. You use could like this to say that it is not possible for someone or something to have more of a particular quality.
I couldn’t be happier.
You couldn’t be more wrong.
The setting couldn’t have been lovelier.
He could hardly have felt more ashamed of himself.
talking about the future
5.128 The following paragraphs explain how modals are used when you are talking about possible future situations. The uses of must, cannot, could, might, and may are similar to their uses when you are talking about possible situations in the present.
certainty: will
5.129 You use will to say that something is certain to happen or be the case in the future.
They will see everything.
The price of food will go up.
The service will have been running for a year in May.
Be going to can also be used to say that something is certain to happen in the future. This use of be going to is dealt with in paragraph 5.231.
certainty: shall, must, and cannot
5.130 Shall is also used to say that something is certain to happen. You usually use shall when you are talking about events and situations over which you have some control. For example, you can use shall when you are making a resolution or a promise.
I shall be leaving as soon as I am ready.
Very well, my dear. You shall have the coat.
Of course he shall have water.
‘You’ll make a lot of money.’ – ‘I shall one day.’
You use must to say that something is certain to happen because of particular facts or circumstances.
This research must eventually lead to computer decision-making.
You use cannot to say that something is certain not to happen because of particular facts or circumstances. You do not use must not.
A team cannot hope to win consistently without a good coach.
The bad weather can’t last.
expectation: should and ought to
5.131 You use should or ought to to say that you expect something to happen.
She should be back any time now.
This course should be quite interesting for you.
The Court of Appeal ought to be able to help you.
It ought to get better as it goes along.
Should and ought to are also used when you are talking about the importance of doing something. This use is explained in paragraph 5.213.
future possibility: could, might, and may
5.132 You use could, might, or may to say that it is possible that a particular thing will happen.