Numerical integration (Trapezoidal rule)

The system must follow the requirements:

1. System must provide a range of functions, including continuous ones and those with discontinuity.
2. System must provide calculations if there is no discontinuity on the chosen range of a function.
3. System must provide calculations if there is a removable discontinuity on the chosen range of a function.
4. System must restrict calculations if there is any other discontinuity on the chosen range of a function.
5. System must provide the user with possibility of choosing number of partitions.

Removable discontinuity is avoided by taking an algorithmic mean value Y (𝑓(𝑥−𝜀),𝑓(𝑥+𝜀), 𝜀 - small constant).

Program must validate data and inform the user about errors.

Output example:

Flowchart: