How to convert an user-input into a function in python 2.7

Question

I am pretty new to programming but I want to define a function like the following with user input:

function = raw_input('What function shall be used? ')     #user puts in "(1+1/x)^x"
def f(x):                                                 #using this to define
    y = (1+1/x)**x     
    return y

I hope it is clear what I try to do. Could you use input and define a priori that sin is used as math.sin ? But how do I define the function afterwards?

Edited to add specification from the comments

Let's say the valid input is python code such as "(1+1/x)**x" like in the question. Could you now use eval to define a function f(x) which can be later used?

Answer 1

As I commented, this can be done with something like eval , but is unsafe because you should never trust random user input.

>>> def expr_to_fn(expr):
...    expr = expr.replace('^', '**')
...    symbols = set(re.findall(r'([A-Z,a-z]+)', expr))
...    fn = eval("lambda {}: {}".format(",".join(symbols), expr))
...    return fn

>>> f = expr_to_fn("(1+1/x)^x")
>>> f(2)
2.25

The safe way is to implenet a DSL and a parser, or use a CAS (computer algebra system) like sympy, as suggested by Hiro.