Suppose there's a cycle $\displaystyle \alpha = (3714)$ in $\displaystyle S_7$ where $\displaystyle S_7$ is a symmetric group on a set $\displaystyle \{1, 2, \cdots, 7\}$

What is $\displaystyle \alpha^2$?

Is it composition of $\displaystyle \alpha$ like this $\displaystyle \alpha \circ \alpha$?

I'm asking this because suppose there's a function $\displaystyle f(x) = x + 1$

Now, $\displaystyle (f(x))^2 = (x + 1)^2$ whereas $\displaystyle (f \circ f)(x) = (x + 1) + 1$

which are completely two different things.

So what is the meaning of $\displaystyle \alpha^2$(square of a cycle) in abstract algebra?