Let $\alpha\in A_{c}^{n,n}(W)$ for an open subset $W$ of ${X^{\rm an}}$, where $n:=\dim(X)$. Obviously, we may view $\alpha$ as a $(n,n)$-form on ${X^{\rm an}}$ with compact support. We call a very affine open subset $U$ as in Proposition 5.13 a very affine chart of integration for $\alpha$. Then $\alpha$ is given by a superform $\alpha_{U}\in A_{c}^{n,n}({\rm Trop}(U))$. We define the integral of $\alpha$ over $W$ by

$$\int_{W}\alpha:=\int_{{\rm Trop}(U)}\alpha_{U}.$$

Here, we view ${\rm Trop}(U)$ as a tropical cycle (see 4.6) and we integrate as in 3.4.