Evaluating a mathematical expression in a string

eval is evil

eval("__import__('os').remove('important file')") # arbitrary commands
eval("9**9**9**9**9**9**9**9", {'__builtins__': None}) # CPU, memory

Note: even if you use set __builtins__ to None it still might be possible to break out using introspection:

eval('(1).__class__.__bases__[0].__subclasses__()', {'__builtins__': None})

Evaluate arithmetic expression using ast

import ast
import operator as op

# supported operators
operators = {ast.Add: op.add, ast.Sub: op.sub, ast.Mult: op.mul,
             ast.Div: op.truediv, ast.Pow: op.pow, ast.BitXor: op.xor,
             ast.USub: op.neg}

def eval_expr(expr):
    """
    >>> eval_expr('2^6')
    4
    >>> eval_expr('2**6')
    64
    >>> eval_expr('1 + 2*3**(4^5) / (6 + -7)')
    -5.0
    """
    return eval_(ast.parse(expr, mode="eval").body)

def eval_(node):
    if isinstance(node, ast.Num): # <number>
        return node.n
    elif isinstance(node, ast.BinOp): # <left> <operator> <right>
        return operators[type(node.op)](eval_(node.left), eval_(node.right))
    elif isinstance(node, ast.UnaryOp): # <operator> <operand> e.g., -1
        return operators[type(node.op)](eval_(node.operand))
    else:
        raise TypeError(node)

You can easily limit allowed range for each operation or any intermediate result, e.g., to limit input arguments for a**b:

def power(a, b):
    if any(abs(n) > 100 for n in [a, b]):
        raise ValueError((a,b))
    return op.pow(a, b)
operators[ast.Pow] = power

Or to limit magnitude of intermediate results:

import functools

def limit(max_=None):
    """Return decorator that limits allowed returned values."""
    def decorator(func):
        @functools.wraps(func)
        def wrapper(*args, **kwargs):
            ret = func(*args, **kwargs)
            try:
                mag = abs(ret)
            except TypeError:
                pass # not applicable
            else:
                if mag > max_:
                    raise ValueError(ret)
            return ret
        return wrapper
    return decorator

eval_ = limit(max_=10**100)(eval_)

Example

>>> evil = "__import__('os').remove('important file')"
>>> eval_expr(evil) #doctest:+IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
TypeError:
>>> eval_expr("9**9")
387420489
>>> eval_expr("9**9**9**9**9**9**9**9") #doctest:+IGNORE_EXCEPTION_DETAIL
Traceback (most recent call last):
...
ValueError: