Horizontal Slicing in Integral

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You can use SymPy a bit more easily here by integrating from d to 1/1^2 (the top half), so there is no need to adjust for the bottom rectangle, as the median is above 1/6^2:

julia> a, b = 1, 6
A =(1, 6)

julia> @syms x
(x,)

julia> A = integrate(1/x^2, (x, a, b))
5/6

julia> @syms c
(c,)

julia> solve(integrate(1/x^2, (x, a, c)) ~ A/2, c)
1-element Vector{Sym}:
 12/7

julia> @syms d
(d,)

julia> # y = 1/x^2 -> x = 1/sqrt(y)

julia> @syms y
(y,)

julia> solve(integrate(1/sqrt(y), (y, d, 1)) ~ A/2)
1-element Vector{Sym}:
 361/576
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