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This third volume of the Numerical and Algorithmic Approaches to Integrals series focuses on error analysis, precision, and comparison of major numerical integration methods applied to analytically solvable integrals. Combining theoretical rigor with practical Python implementation, the book offers a systematic study of absolute and relative errors, algorithm design, and guided, corrected exercises. Each method follows a consistent structure: theoretical foundations, precision estimation, algorithm development, and hands-on application. Designed for students in the sciences, as well as researchers and engineers, this volume helps consolidate numerical analysis skills through an autonomous, progressive, and comparative reading experience. It serves as a valuable resource for mastering the reliability of numerical methods in academic and professional settings that demand both precision and analytical depth.