max(a_ and b_) := max(a,b); max(a_ * b_) := If(a>0, a*max(b), If(a<0, a*min(b) )); max(a_ + b_) := max(a)+max(b); max(a_ - b_) := max(max(a)-max(b), max(a)+max(b)); max(-x_^2):=0; max(e^x_):=oo; max(sin(x_)):=1; max(cos(x_)):=1; max(tan(x_)):=oo; max(cot(x_)):=oo; max(sec(x_)):=oo; max(csc(x_)):=oo; max(asin(x_)):=oo; max(acos(x_)):=oo; max(atan(x_)):=pi/2; max(acot(x_)):=pi/2; max(asec(x_)):=pi/2; max(acsc(x_)):=pi/2; max(sinh(x_)):=oo; max(cosh(x_)):=oo; max(tanh(x_)):=1; max(coth(x_)):=oo; max(sech(x_)):=1; max(csch(x_)):=oo; max(asinh(x_)):=oo; max(acosh(x_)):=oo; max(atanh(x_)):=oo; max(acoth(x_)):=oo; max(asech(x_)):=oo; max(acsch(x_)):=oo; max(exp(x_)):=oo; max(log(x_)):=oo;