If one types

seq(cos((n mod 3)*Pi,n=2..13);

Maple returns, correctly,

1,1,-1,1,1,-1,1,1,-1,1,1,-1

If one types

sum(cos((n mod 3)*Pi),n=2..13);  # surely the sum of the above sequence = 4

Maple returns, incorrectly, the value 1.

Sure enough, if one types

sum(cos((n mod 3)*Pi)*exp(n),n=2..13); # expecting the sum of e^n with every third term negative

Maple returns

e^2-e^3+e^4-e^5+e^6-e^7+e^8-e^9+e^10-e11+e^12-e^13  ...