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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | import Mathlib
namespace OAI
noncomputable section
namespace CylinderCovering.GeneralCapArea
def profile (q : ℝ) : ℝ := (q ^ 2 + q ^ 4) / 16
def idealSpeed (q : ℝ) : ℝ := ((1 + q ^ 2) / 4) ^ 2 + 2 * (q / 2) ^ 2
def idealDensity (ε η q : ℝ) : ℝ :=
1 / 4 + ε ^ 2 * (profile q + η - idealSpeed q / 8)
def capDensity (ε α β : ℝ) (R : ℝ → ℝ) (q : ℝ) : ℝ :=
(R q) ^ 2 / Real.sqrt (1 + ε ^ 2 * (α ^ 2 + 2 * β ^ 2))
end CylinderCovering.GeneralCapArea
end
end OAI
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