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Problem: Multi$-$dimensional Range Sum

You are given a $2$D matrix of integers matrix and a set of queries. Each query is represented by four integers $($row$1,$ col$1,$ row$2,$ col$2),$ which denote the top$-$left and bottom$-$right coordinates of a submatrix. Your task is to find the sum of all elements within each submatrix specified by the queries.

Write a function range$\_$sum$\_$queries$($matrix$,$ queries$)$ that takes in the following parameters:

matrix: a $2$D list of integers representing the matrix.

queries: a list of tuples, where each tuple represents a query $($row$1,$ col$1,$ row$2,$ col$2).$

The function should return a list of integers, where each integer represents the sum of elements within the corresponding submatrix specified by the queries.