How do I use an if statement in sympy so that I can repeatedly go to the next() iterable in my iterator everytime?

Question

I'm coding in python and I'm having an issue with my sympy summation. I want to use my sympy summation so that I can call next() everytime the value of x (which is my symbol) changes.

The problem is that when I use next() the function only moves once and stays the same for the whole summation.

I want the value of num to go from 1 to 2 to 3 to 4 and so on since that's what happens when you repeatedly call next(), everytime the value of x goes up.

I already coded an iterator that lets me control when to move forward with next() and when not to so I know this is possible. My code is below:

from sympy import summation, Eq, symbols

x = symbols('x')

class DynamicIterator:
    def __init__(self, func, a, b):
        self.func = func  # Function to generate values
        self.counter = 0  # Keeps track of the current index
        self.a = a
        self.b = b
        self.can_advance = True  # Default to allowing automatic advancement
        self.advanced = False  # Flag to control when to advance

    def __iter__(self):
        return self

    def __next__(self):
        if not self.can_advance:
            raise StopIteration  # Stop iteration if cannot advance

        value = self.func(self.counter, self.a, self.b)  # Generate the value
        self.counter += 1  # Increment the counter
        return value

    def control_advance(self, can_advance):
        """Control whether the iterator can advance or not."""
        self.can_advance = can_advance

    # Define the function that returns the value of `l`


def generate_combinations(n, a, c):
    range_size = c - a + 1
    p = a + (n // range_size)
    l = a + (n % range_size)
    return l  # Only return `l`

    # Parameters for `a` and `b`

# Create an instance of the iterator
expressions = DynamicIterator(generate_combinations, 1, 256 - 1)

# Define a lambda to get the next value of `l`
next_expr = lambda: next(expressions)
#print(next_expr())
# expressions.control_advance(True)
#print(next_expr())

if x != 0:
    num = int(next_expr())
else:
    num = 1

formula = num + x

total = summation(formula, (x, 1, 3))
print(total)

As you can see in this code, I'm just simply adding num to x. The value of num should change from 1 to 2 to 3 since it should be calling next() each time. I want this to occur everytime x in the summation changes values and goes up by 1.

I specifically want my code like this guys and I don't want any for loops or any other type of loops. I want everything closed form so I can use it in other projects too. Can someone show me what to do?

if x != 0:
    num = int(next_expr())
else:
    num = 1

right here is where i want it. I want it to say that num value is the next value everytime x the symbol goes up.