from operator import add, sub, mul, truediv

OPERATORS = {'+': (add, 0), '-': (sub, 0),
             '*': (mul, 1), '/': (truediv, 1)}


def calc_in_polish(exp: list) -> float:
    """
    >>> calc_in_polish([5, 2, '*', 10, 5, '*', '+'])
    60.0
    """
    stack = []
    for i in exp:
        operation = OPERATORS.get(i)
        if operation:
            a = stack.pop()
            b = stack.pop()
            stack.append(operation[0](b, a))
        else:
            stack.append(i)

    return stack.pop()


def str_to_exp(raw_exp: str) -> list:
    """
    >>> str_to_exp('1 + 22.0 * 110')
    [1.0, '+', 22.0, '*', 110.0]
    """
    res = []
    tmp_num = ''
    for i in raw_exp:
        if i.isnumeric() or i == '.':
            tmp_num += i
        elif i in OPERATORS or i in '()':
            if tmp_num:
                res.append(float(tmp_num))
                tmp_num = ''
            res.append(i)

    if tmp_num:
        res.append(float(tmp_num))

    return res


def to_polish(exp: list) -> list:
    """
    >>> to_polish([5, '*', 2, '+', 10, '*', 5])
    [5, 2, '*', 10, 5, '*', '+']
    """
    op_stack = []
    result = []
    for token in exp:
        if type(token) is float:
            result.append(token)
        elif token in OPERATORS:
            while op_stack and op_stack[-1] != '(' and OPERATORS[token][1] <= OPERATORS[op_stack[-1]][1]:
                result.append(op_stack.pop())
            op_stack.append(token)
        elif token == ')':
            while op_stack:
                op = op_stack.pop()
                if op == '(':
                    break
                result.append(op)
        elif token == '(':
            op_stack.append(token)

    result.extend(op_stack[::-1])
    return result


def calc(raw_exp: str) -> float:
    """
    >>> _eval('5 * 2 + 10 * 5')
    60.0
    """
    exp = str_to_exp(raw_exp)
    polish = to_polish(exp)
    res = calc_in_polish(polish)

    print('raw:\t', raw_exp)
    print('parsed:\t', exp)
    print('polish:\t', polish)
    print('result:\t', res)

    return res


calc('5 * (2 + 10) * 5')