[meyer]

Yes, SHALL and WILL are mandatory words, should and May are words that are desired if possible but NOT mandatory.

I think that "should" is stronger than "may".
I may ride my bicycle tomorrow. Or I may not.
I should ride my bicycle tomorrow. It would be helpful in gaining fitness. It's a preferred choice.
Shall and will are both affirmations. I will ride my bike tomorrow. No wiggle room, no reasonable alternative.

[No_Doll_i]

Unless you wake up and it’s raining and you say screw it I am NOT riding my bike today and promptly return to bed. ;-)

[Billyv]

Military definitions.