Since $x$, $y$, and $z$ are nonnegative real numbers, we have $x \leq 1$, $y^2 \leq y$, and $z^3 \leq z$.
Adding these inequalities gives $x + y^2 + z^3 \leq x + y + z = 1$.
Equality occurs when $x = 1$, $y = 0$, and $z = 0$.
Therefore, the maximum value of $x + y^2 + z^3$ is $\boxed{1}$.The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Given that $x$, $y$, and $z$ are nonnegative real numbers and $x + y + z = 1$, what is the maximum value of $x + y^2 + z^3$?

### Answer:
