Shadeop is a term used in computer graphics rendering to refer to an atomic, built-in function used in a shader.
It is a portmanteau that blends the terms shading and operation.
The term is specifically used in the context of shaders written in the RenderMan Shading Language (RSL) for use with RenderMan-compliant renderers.
User-defined functions written in RSL are just referred to as "functions". Hence, use of the term mostly serves as a means to distinguish the latter type from built-in type functions.
RSL also allows for binary plugins written in C to be loaded and treated like built-in shadeops. These are commonly referred to as DSO shadeops. Two RenderMan implementations, 3Delight and PhotoRealistic RenderMan, have recently added new type in recent years called RSL plugin shadeop. This type uses a newer C++ API but otherwise can't be distinguished from the older type by a user, when called from within a shader.
The following example shader makes use of the ambient(), diffuse(), faceforward(), normalize() and transform() built-in shadeops as well as the checkerboard() user-defined RSL plugin shadeop.