It has been shown that the integral,
$$ \int_0^1 x^{-x}dx \label{eq:1} \tag{1}$$
is equivalent to
$$ = \sum_{x \ge 0}{x^{-x}} \label{eq:2} \tag{2}$$
It has also shown that this converges to a finite value.
So let's define $ f(x) = x^{-x} $, this means that
$$ \int_0^1 f(x)dx = f(0) + f(1) + f(2) \dots \label{eq:3} \tag{3}$$
Let's call functions that obey \eqref{eq:3} "Height and Area symmetric"
Are there other functions that follow this height and area symmetry while still converging to a finite value, or is this the only function that follows this rule?