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var('x,y,z') 
plot3d(lambda x,y :min(y,x),(x,0,1),(y,0,1))

gives a reasonable plot (if you rotate the plot manually)

var('x,y,z') 
 plot3d(lambda x,y :min(y,x),(x,0,1),(y,0,1))

gives a reasonable plot (if you rotate the plot manually)manually).

from mpmath import *
mp.dps = 15; mp.pretty = True
f = lambda x,y,z: min(x,y,z)
quad(f,[0,1],[0,1],[0,1])

var('x,y,z') plot3d(lambda x,y :min(y,x),(x,0,1),(y,0,1))

gives a reasonable plot (if you rotate the plot manually).

Numerical integration with mpmath:

from mpmath import *
mp.dps = 15; mp.pretty = True
f = lambda x,y,z: min(x,y,z)
quad(f,[0,1],[0,1],[0,1])