I think these are bugs in parse_expr.  Sorry, my python expertise is 
insufficient to determine what is going on.

In [80]: 
transformations=standard_transformations+(convert_xor,implicit_multiplication_application)

In [81]: parse_expr("sin^2 (3x*E^(x))", transformations=transformations)
Out[81]: 
   ⎛     ⎛ x⎞⎞
   ⎜     ⎝2 ⎠⎟
sin⎝3⋅x⋅ℯ    ⎠

In [82]: parse_expr("sin^2 (3*E^(x))", transformations=transformations)
  File "<string>", line 1
    sin (Integer (3 )*(E (Symbol ('x' )))**Integer (2 )**)
                                                         ^
SyntaxError: unexpected EOF while parsing

In [84]: parse_expr("sin**2(E^(x))", transformations=transformations)
Out[84]: 
   ⎛ ⎛ x⎞⎞
   ⎜ ⎝2 ⎠⎟
sin⎝ℯ    ⎠

In [85]: parse_expr("sin**2(E^(3x))", transformations=transformations)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/home/nykamp/src/sympy/<ipython-input-85-c37d30812cac> in <module>()
----> 1 parse_expr("sin**2(E^(3x))", transformations=transformations)

/home/nykamp/src/sympy/sympy/parsing/sympy_parser.pyc in parse_expr(s, 
local_dict, transformations, global_dict)
    712 
    713     code = stringify_expr(s, local_dict, global_dict, 
transformations)
--> 714     return eval_expr(code, local_dict, global_dict)

/home/nykamp/src/sympy/sympy/parsing/sympy_parser.pyc in eval_expr(code, 
local_dict, global_dict)
    650     """
    651     expr = eval(
--> 652         code, global_dict, local_dict)  # take local objects in 
preference
    653 
    654     return expr

/home/nykamp/src/sympy/<string> in <module>()

TypeError: 'Exp1' object is not callable



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