Must, have to and should: (Modals)

You must do your homework.
You must wipe your feet before you enter.
MUST: obligation is imposed by the speaker. The speaker has authority over the one that is spoken to and he/she exercises his/her power.
Must is also preferred to refer to ourselves (I must go now) and to express a strong advice or invitation (That's a picture you really must see).

You have to pass your exams if you want to succeed.
In England you have to drive on the left.
HAVE TO: obligation springs from circumstances or external rules. Something has to be done, whether the speaker likes it or not.

You should quit smoking.
You should remember these rules.
SHOULD is used to give advice. No obligation here, rather a recommendation from the speaker