Integrating quadruple integral ?

I am trying to integrate a quadruple integral with the following limit of integration

I am using the integralN.m function from Mike Hosea as follow

clear all;
syms w z y x real;
wmin = 0;
wmax = @(z) z;

zmin = 0;
zmax = @(y)  y;

ymin = 0;
ymax = @(x)  x;

xmin = 0;
xmax = Inf;

temp = -(x^2 + y^2 + z^2 + w^2)/2;
f_symbol = exp(temp);
f = matlabFunction(f_symbol)

 q4 = integralN(f,wmin,wmax,xmin,xmax,ymin,ymax,zmin,zmax,'AbsTol',1e-5,'RelTol',1e-3)

And receive the following error

 Error using integral2 (line 76)
XMAX must be a floating point scalar.

Error in integralN>integral4 (line 139)
q = integral2( ...

Error in integralN (line 92)
        q = integral4(f,varargin{:});

Error in myprogram (line 34)
 q4 = integralN(f,wmin,wmax,xmin,xmax,ymin,ymax,zmin,zmax,'AbsTol',1e-5,'RelTol',1e-3)

I am having a feeling that this error come from the order of integration wmin,wmax,xmin,xmax,ymin,ymax,zmin,zmax

So my second attempt is as follow

 syms w z y x real;
wmin = 0;
wmax = @(z) z;

zmin = 0;
zmax = @(y)  y;

ymin = 0;
ymax = @(x)  x;

xmin = 0;
xmax = Inf;

temp = -(x^2 + y^2 + z^2 + w^2)/2;
f_symbol = exp(temp);
fun1 = matlabFunction(f_symbol,'Vars',[x,y,z,w])


q = integralN(fun1,xmin,xmax,ymin,ymax,zmin,zmax,wmin,wmax,'AbsTol',1e-3,'RelTol',1e-3)

This lead to another error

Error using myprogram>@(y)y
Too many input arguments.

Error in
integralN>@(x,y)integral2(@(z,w)f(x*ones(size(z)),y*ones(size(z)),z,w),zmin(x,y),zmax(x,y),@(z)wmin(x*ones(size(z)),y*ones(size(z)),z),@(z)wmax(x*ones(size(z)),y*ones(size(z)),z),varargin{9:end},method_override{:})
(line 135)
    zmax(x,y), ...

Error in integralN>@(xv,yv)arrayfun(inner,xv,yv) (line 140)
    @(xv,yv)arrayfun(inner,xv,yv), ...

Error in integral2Calc>@(y)fun(xi*ones(size(y)),y) (line 18)
    @(y)fun(xi*ones(size(y)),y),y1i,y2i,opstruct.integralOptions), ...

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in
integral2Calc>@(xi,y1i,y2i)integralCalc(@(y)fun(xi*ones(size(y)),y),y1i,y2i,opstruct.integralOptions)
(line 17)
innerintegral = @(x)arrayfun(@(xi,y1i,y2i)integralCalc( ...

Error in
integral2Calc>@(x)arrayfun(@(xi,y1i,y2i)integralCalc(@(y)fun(xi*ones(size(y)),y),y1i,y2i,opstruct.integralOptions),x,ymin(x),ymax(x))
(line 17)
innerintegral = @(x)arrayfun(@(xi,y1i,y2i)integralCalc( ...

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 83)
        [q,errbnd] = vadapt(@AToInfInvTransform,interval);

Error in integral2Calc>integral2i (line 20)
[q,errbnd] = integralCalc(innerintegral,xmin,xmax,opstruct.integralOptions);

Error in integral2Calc (line 7)
    [q,errbnd] = integral2i(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in integralN>integral4 (line 139)
q = integral2( ...

Error in integralN (line 92)
        q = integral4(f,varargin{:});

Error in myprogram (line 36)
q = integralN(fun1,xmin,xmax,ymin,ymax,zmin,zmax,wmin,wmax,'AbsTol',1e-3,'RelTol',1e-3)

Please help me overcome this issue

Thank you for your enthusiasm !

Answer 1

[Tuong Nguyen Minh]

I have been able to deduce the answer after much frustration. The corresponding syntax should be

clear all;
clc;
syms w z y x real;
wmin = 0;
wmax = @(x,y,z) z;

zmin = 0;
zmax = @(x,y)   y;

ymin = 0;
ymax = @(x)   x;

xmin = 0;
xmax = Inf;

temp = -(x*x + y*y + z*z + w*w)/2;
f_symbol = exp(temp);
fun1 = matlabFunction(f_symbol,'Vars',[x,y,z,w])


q = integralN(fun1,xmin,xmax,ymin,ymax,zmin,zmax,wmin,wmax,'AbsTol',1e-3,'RelTol',1e-3)