Abstract: This paper presents a Modified Formula for Cotes rule with fifths derivatives of endpoint and its truncation error. It also displays an analysis on convergence order of compound formula. Though compound modified formula for Cotes rule with endpoint derivatives just calculates a newly-added fifths derivative of the two endpoints for each time compared with compound Cotes formula calculation, there are 2 more ranks of the convergence order in this modified formula. Examples of numerical calculation have validated theoretical analysis. 

Key words: numerical integration, algebraic precision, truncation error, order of convergence