What is the Name of the Function $f(x) = \frac{x + |x|}{2}$

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I'm dealing with a function that can be written in all of the following forms:

$$f(x) = \frac{x + |x|}{2} \\ = x\ \Theta(x) \\ = \int_{-\infty}^x \Theta(y) \operatorname{d}y,$$

where $\Theta(x)$ is the standard unit step (Heaviside) function. Does the function $f(x)$ have a special name?