Festival around the world

is supposed to                            =…should…
(be) able to ability, less used than can
e.g. i’m not able to come to the game on friday.
can
 
  ability
e.g. can you play the piano?
 asking for and giving permission
 e.g. “mom, can i go the cinema tonight?”
“no, you can’t.  you have homework to do”
 offer
e.g.  can i help you?
 request, instruction
e.g.  can you switch on the light for me?
 capability
e.g. the summers in england can be really unpredictable.
 with be to make criticisms
e.g. susan can be a real pa in in the neck at times.
can’t
  ability
e.g. i can’t come to the game on friday.
 when you feel sure something is not possible (opposite of must)
e.g.  the tennis match ca n’t be over yet.  (i’m sure it isn’t).
could
 
  possibility or uncertainty (can also use might)
e.g. he could be the one for you!
 request (more polite than can)
e.g. could you switch on the light for me?
 suggestion
  e.g. we could go on a picnic this afternoon.
 asking for and giving permission
  e.g. “could i use yo ur phone?”
“yes, of course you can”
 unwillingness
  e.g. i couldn’t possibly leave tom alone while he ’s in this state.
 with comparative adjectives to express possibility or impossibility 
e.g. i could be  fitter.
e.g. he couldn’t study harder.
had better strong advice (less used than should)
  e.g. you’d better do the washing up now.
e.g. i’d better not go out tonight, because i have to get up early tomorrow.
may
 
  to express although in clauses
  e.g. i may be married to you, but that doesn’t give you the right to treat me like dirt.
 possibility or uncertainty (formal)
  e.g. there may be a cure for aids within the next ten years.
 asking for and giving permission (less usual, more formal) 
e.g. “may i use your phone?”
“yes, of course you may”
may as well/might as well describes the only thing left to do, something which the speaker is no t enthusiastic about
  e.g. i’m so bored, i may as well do some housework.
might
  possibility or uncertainty
  e.g. there might be a cure for aids within the next ten years.
 unreal situation
e.g. if i knew her better, i might invite her to the ball.
must
 
  when you feel sure something is true (opposite of can’t)