“How does addition work?" Isn't it the same as stacking rocks one on top of the other? And repeated addition? Isn't that called multiplication? But then, even if you were to slice many rocks in half, could you ever multiply half with half? Maybe three-fifths with three-fifths? Why did multiplication get so significantly complex when you ran out of natural numbers?

Your crew stops before a natural footbridge in the cavern. It is narrow, has no protection ,and to fall from there would be fatal. Juee breaks the silence, presenting a new clue glowing in jade green behind you. She's optimistic that there is a way to cross the bridge unscathed if you can solve it.

Define the function $\Omega$ over as follows, over those complex numbers $z$ whose real part is positive. $$ \Omega (z) = \frac{1}{z}\prod_{n=1}^{\infty}\frac{\left(1+\frac{1}{n}\right)^z}{1+\frac{z}{n}} $$

What is the value of the following expression? $$ 1+\left(\frac{\Omega(5)}{2}\right)^3. $$