宿題をやるべきだったのに。

homework

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to do; to undertake; to perform; to play (a game); to study; to send; to dispatch; to despatch; to put; to move; to turn (one's head, glance, etc.); to give (esp. to someone of equal or lower status); to let have; to present; to bestow; to confer; to make (a vehicle) go faster; to run (a business); to keep; to be engaged in; to practice (law, medicine, etc.); to practise; to have (food, drink, etc.); to eat; to drink; to smoke; to hold (a performance); to perform; to show; to ease (one's mind); to harm; to injure; to kill; to have sex with; to live; to get by; to get along; to do ... completely; to do ... broadly; to do ... to a great distance; to do ... for (someone of equal or lower status); to do ... to (sometimes with negative nuance); to make active efforts to ...

shall; should; must

be; is; indicates past or completed action; indicates light imperative

although; when; and yet; despite this; in spite of; even though; but even so; but even then; however; nevertheless; for all that; notwithstanding that; while; if only; I wish; I tell you; you should do; in order to