restart:

a := [0, 1/2, 1]:
f    := product((abs(4 * x[i] - 2) + a[i]) / (1 + a[i]), i=1..3):
mu   := int(int(int(f, x[1]=0..1), x[2]=0..1), x[3]=0..1):
f1   := int(int(f, x[2]=0..1), x[3]=0..1) - mu:
f2   := int(int(f, x[3]=0..1), x[1]=0..1) - mu:
f3   := int(int(f, x[1]=0..1), x[2]=0..1) - mu:
f12  := int(f, x[3]=0..1) - mu - f1 - f2:
f23  := int(f, x[1]=0..1) - mu - f2 - f3:
f31  := int(f, x[2]=0..1) - mu - f3 - f1:
f123 := f - mu - f1 - f2 - f3 - f12 - f23 - f31:
var  := int(int(int(f^2, x[1]=0..1), x[2]=0..1), x[3]=0..1) - mu^2:
D1   := int(f1^2, x[1]=0..1):
D2   := int(f2^2, x[2]=0..1):
D3   := int(f3^2, x[3]=0..1):
D12  := int(int(f12^2, x[1]=0..1), x[2]=0..1):
D23  := int(int(f23^2, x[2]=0..1), x[3]=0..1):
D31  := int(int(f31^2, x[3]=0..1), x[1]=0..1):
D123 := int(int(int(f123^2, x[1]=0..1), x[2]=0..1), x[3]=0..1):
S1   := D1 / var:
S2   := D2 / var:
S3   := D3 / var:
S12  := D12 / var:
S23  := D23 / var:
S31  := D31 / var:
S123 := D123 / var:
m    := [mu, evalf(mu)];
v    := [var, evalf(var)];
s1   := [S1, evalf(S1)];
s2   := [S2, evalf(S2)];
s3   := [S3, evalf(S3)];
s12  := [S12, evalf(S12)];
s23  := [S23, evalf(S23)];
s31  := [S31, evalf(S31)];
s123 := [S123, evalf(S123)];

