When reading Problems in Calculus of One Variable (a translated Russian book), I came across unfamiliar notation "$E(x)$". It is neither expected value nor $\exp(x)$. Here is a picture of the function used in context, which I hope someone can deduce what it means from
$$\int\limits_0^x E(x)\mathrm d x=\frac{E(x)(E(x)-1)}{2}+E(x)[x-E(x)]$$
It is not defined in the book, nor specific to context, and also used in multiple instances.
On
$E(x)$ the floor or the greatest integer function : $E(x)=[x]$, $x=[x]+q$, where $[x]$ is integer $n$ and $q=x-[x]$ is the fractional part. $$S=\int_{0}^{x} [t] dt=\int_{0}^{1} 0 dt+ \int_{1}^{2} 1 dt+\int_{2}^{3} 2 dt+.......+\int_{n-1}^{n} (n-1) dt+\int_{n}^{n+q} n dx$$ $$S=1+2+3+4+...+(n-1)+nq=n(n-1)+nq=n(n-1)/2+nq$$ $$ \implies S=[x]([x]-1)/2+[x](x-[x]).$$
I think it is the floor, $E(x) = \lfloor x\rfloor$. If $x$ is an integer, then you find the expression for the sum of integers, and if $x$ is not an integer, you add the missing part of the rectangle. In French, the notation $E(x)$ is used for the floor since it is called "partie entière".