  The Compositional Integral is defined, formally constructed, and discussed. A
direct generalization of Riemann's construction of the integral; it is intended
as an alternative way of looking at First Order Differential Equations. This
brief notice aims to: familiarize the reader with a different approach to
integration, fabricate a notation for a modified integral, and express a
startling use for infinitely nested compositions. Taking inspiration from
Euler's Method for approximating First Order Differential Equations, we
affiliate the method with Riemann Sums; and look at it from a different, modern
angle.
