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will vt; pt would (modal verb), the form is more polite than could. Would you please do (something)(do this and do that)? "polite" is in good manners and consideration for other people, not ordering people, but a polite remark, a polite request ,an impatient request, a wish.
eg:-Woud you like to take a seat? Would you mind my request for a favour?(no need to cause an offence against good manners, causing inconvenience to)
eg:-They have been at great inconvenience in order to help the refugees as much as they "could".
eg:-Let him do what he will. Would you please do something ?
eg:-What would you do? Would you please come back later?Would you please come in ?Would you please sit down ?
eg:-Would (=I would) to her that I had agreed !
eg:-Come whenever you will (wish to come).
---Would replaces will to show future in the past:-
eg:-I wonder whether cooked rice will be ready.
eg:-I wondered whether cooked rice would be ready in the past.
eg:-You would have been in Bejing this time yesterday.
eg:-I said I would do it.
eg:-We said we would give them some money+foodstuffs.
can finite verb; pt=could; indicating ability or capacity to do something, be able to; know how to, Can you lift this heavy parcel DHL ?
Could refers to ability or capacity in past time:-When Grandma was young, she could cook the "Peking duck".She could read Japanese and Korean when after studying.
Could is used in "if" -clause to indicate a condition, expressed or implied:-Could you lift that heavy parcel DHL now, if you tried ,please.? Could you have lifted that heavy parcel DHL if you had tried this noon ? Could is not used , except in conditional. Instead, be able to, manage to, succeed in doing something are preferred.Could is used for the past time:-We could hear someone called the spy talking in the next room.We could see a gun on the secret agent's floor..She said she could smell something burning.Could may replace can in a tentative request in question form:-eg:-You could(=may) go home now--Could you please ?The children asked whether they could (=might) go for a game.Could you please stop them ? Could in questions with what-ever, where, how to indicate surprise, bewilderment, im-patience, etc., according to the context. What could he "mean" ?What could we do about it? Where could they have got to ? How could you be so unkind ---so cruel---don't be cruel please.Could you please(....) ?