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Your Mathematica input is slightly off. Here's what you want:
Assuming[y > 0, Integrate[Log[10, Sqrt[x^2 + y^2]], {x, -10, -1}]]
This gives an answer with the same absolute value as Sage, but the latter returns an odd extra minus sign. You'll get the same answer for both if you change the variable of integration:
integral(log(sqrt(x^2+y^2),10),x,1,10)
