double and triple integrals implementation we follow the ideas for the implementations of the midpoint rule for double integral the corresponding functions are shown below and found in the file midpoint_triple py def midpoint_triple (gabcdefnxnynz)hx ( )/float(nxhy ( )/float(nyhz ( )/float(nzi for in range(nx)for in range(ny)for in range(nz)xi hx/ *hx yj hy/ *hy zk hz/ *hz +hx*hy*hz* (xiyjzkreturn def midpoint(fabn) float( - )/ result for in range( )result + (( / *hresult * return result def midpoint_triple (gabcdefnxnynz)def (xy)return midpoint(lambda zg(xyz)efnzdef ( )return midpoint(lambda yp(xy)cdnyreturn midpoint(qabnxdef test_midpoint_triple()"""test that linear function is integrated exactly ""def (xyz)return * * - import sympy xyz sympy symbols(' 'i_expected sympy integrateg(xyz)(xab)(ycd)(zef)for nxnynz in ( )( )( )i_computed midpoint_triple gabcdefnxnynzi_computed midpoint_triple gabcdefnxnynztol - print i_expectedi_computed i_computed assert abs(i_computed i_expectedtol assert abs(i_computed i_expectedtol if __name__ ='__main__'test_midpoint_triple(