I think when you use ' sb's supposed to do sth', it's his obligation to do it, while using 'should' just means he can do it or not, but he'll be all the better for doing it. Please correct me if I'm wrong.
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whatchadoinI'm supposed to do my homework.Your teacher has assigned it to you. You have an obligation to your teacher to do it. The point of view is on the agent who gave you the responsibility. You do not feel a strong personal obligation.
whatchadoinI should do my homework.It is more a self-imposed obligation because