Do you have a multivariate function which you want to integrate? Do you have a blasé attitude towards executing lambdas instantiated from eval strings? Well then look no further!

arbitrary_integration.py

from inspect import signature
from scipy.integrate import quad


def get_fn_str(fn, lims=(0, 1), existing_string=None, arg_count=0):
    """
    Recursively generate a string which, when evaluated, will integrate an arbitrary function over all of its variables within the given limits.
    """
    if existing_string is None:
        return get_fn_str(fn, lims=lims, existing_string="quad({{}}, {}, {})[0]".format(lims[0], lims[1]), 
                          arg_count=arg_count+1)

    param_list = list(signature(fn).parameters)

    reached_depth = arg_count == len(param_list) - 1

    modified_string = existing_string.format(
        "lambda {}: quad({}, {}, {}{})[0]".format(
            ', '.join(param_list[-arg_count:]),
            fn.__name__ if reached_depth else '{}',
            lims[0],
            lims[1],
            list_to_tuple_str(param_list[-arg_count:])
        )
    )

    if reached_depth:
        return modified_string
    else:
        return get_fn_str(fn, lims=lims, existing_string=modified_string, arg_count=arg_count+1)


def integrate(fn, lims=(0, 1)):
    """
    Integrate an arbitrary function over all of its variables within the given limits.
    """
    return eval(get_fn_str(fn))