A compound machine that operates automatically or by remote control is called a?

A compound machine that operates automatically or by remote control is referred to as a robot. Robots are designed to perform tasks that can be programmed or controlled remotely, making them complex systems that often combine various simple machines and mechanisms to accomplish specific functions.

In contrast to simple machines like levers, which are mechanical devices allowing the movement of loads with minimal effort, or even engines that convert energy into motion but may not operate autonomously, robots have advanced capabilities, including sensors and decision-making processes. Automatons, while they can operate on their own, typically refer to mechanical devices that perform repetitive tasks, rather than continuously adapting to new instructions like modern robots do. Thus, the term 'robot' encompasses the concept of automation and remote control in a way that fits perfectly with the definition provided in the question.