The UserLib6789 library contains more than 850 means of different purpose which eliminate restrictions of a number of standard means of the Maple system or complement their along with expanding Maple software with new tools. In this context, the library can serve as a certain additional tool of programming in Maple, especially useful in the numerous appendices where certain non–standard evaluations have to accompany programming. In addition, means presented in the library have a direct relationship to certain principal questions of programming in the Maple system, not only for the decision of the applied problems but, first of all, for creation of software extending frequently used facilities of the system and/or for eliminating their defects or extending the system with new facilities. The software presented in the library contains a number of rather useful and effective receptions of programming in the Maple system and extends its software that allows programming the problems of various purposes much simply and effectively. The UserLib6789 library not only contains a lot of useful procedures and functions but can serve as a rather useful collection of programming examples using both standard and non–standard techniques of functional–procedural programming in Maple. The UserLib6789 library has an organization similar to the main Maple library, allowing you to work with its tools in the same way as built–in Maple tools.