>>> from sympy import *
>>> x = Symbol('x')
>>> f = cos(acos(x))
>>> f
cos(acos(x))
>>> sin(x).series(x, 4)       # 4 terms of the Taylor series
x - 1/6*x**3 + O(x**4)
>>> dcos = diff(cos(2*x), x)
>>> dcos
-2*sin(2*x)
>>> dcos.subs(x, pi).evalf()  # x=pi, float evaluation
0
>>> I = integrate(log(x), x)
>>> print I
-x + x*log(x)