package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

func readInt(s *bufio.Scanner) int {
	s.Scan()
	i, _ := strconv.ParseInt(s.Text(), 10, 32)
	return int(i)
}

func read5Float64(s *bufio.Scanner) (float64, float64, float64, float64, float64) {
	s.Scan()
	n := strings.Split(s.Text(), " ")
	n1, _ := strconv.ParseFloat(n[0], 64)
	n2, _ := strconv.ParseFloat(n[1], 64)
	n3, _ := strconv.ParseFloat(n[2], 64)
	n4, _ := strconv.ParseFloat(n[3], 64)
	n5, _ := strconv.ParseFloat(n[4], 64)
	return n1, n2, n3, n4, n5
}

func circularSegment(r, theta float64) float64 {
	return r * r * (theta - math.Sin(theta)) / 2
}

func hitFly(scanner *bufio.Scanner) []float64 {
	caseCnt := readInt(scanner)
	answer := make([]float64, caseCnt)
	for i := 0; i < caseCnt; i++ {
		// r fly, r outer ring, thickness, r string and gap length
		f, R, t, r, g := read5Float64(scanner)
		if g <= 2*f {
			answer[i] = 1.
			continue
		}
		rad := R - t - f
		sqrRad := rad * rad
		gridArea := (g - 2*f) * (g - 2*f)
		area := 0.
		for x1 := r + f; x1 < rad; x1 += g + 2*r { // 1st quadrant, x1, y1 is the coord of br
			for y1 := r + f; y1 < rad; y1 += g + 2*r {
				x2, y2 := x1+g-2*f, y1+g-2*f
				if x1*x1+y1*y1 >= sqrRad {
					continue
				}
				switch {
				case x2*x2+y2*y2 <= sqrRad: // All points inside circle
					area += gridArea
				case x1*x1+y2*y2 >= sqrRad && x2*x2+y1*y1 >= sqrRad:
					// Only x1, y1 inside
					area += circularSegment(rad, math.Pi/2-math.Asin(x1/rad)-math.Asin(y1/rad))
					area += (math.Sqrt(sqrRad-x1*x1) - y1) * (math.Sqrt(sqrRad-y1*y1) - x1) / 2
				case x1*x1+y2*y2 >= sqrRad: // x1, y1 and x2, y1 inside
					area += circularSegment(rad, math.Acos(x1/rad)-math.Acos(x2/rad))
					area += ((math.Sqrt(sqrRad-x1*x1) - y1) + (math.Sqrt(sqrRad-x2*x2) - y1)) * (x2 - x1) / 2
				case x2*x2+y1*y1 >= sqrRad: // x1, y1 and x1, y2 inside
					area += circularSegment(rad, math.Asin(y2/rad)-math.Asin(y1/rad))
					area += ((math.Sqrt(sqrRad-y2*y2) - x1) + (math.Sqrt(sqrRad-y1*y1) - x1)) * (y2 - y1) / 2
				default: // All except x2, y2 inside
					area += circularSegment(rad, math.Asin(y2/rad)-math.Acos(x2/rad))
					area += gridArea - (x2-math.Sqrt(sqrRad-y2*y2))*(y2-math.Sqrt(sqrRad-x2*x2))/2
				}
			}
		}
		answer[i] = 1. - area/(math.Pi*R*R/4)
	}
	return answer
}

func main() {
	inputFiles := []string{"C-small-practice.in", "C-large-practice.in", "test.in"}
	outputFiles := []string{"result-small.out", "result-large.out", "test.out"}
	const (
		small = iota
		large
		test
	)

	fileType := large

	fin, _ := os.Open(inputFiles[fileType])
	defer fin.Close()

	scanner := bufio.NewScanner(fin)
	answer := hitFly(scanner)

	fout, _ := os.Create(outputFiles[fileType])
	defer fout.Close()

	for i, ans := range answer {
		s := fmt.Sprintf("Case #%d: %f\n", i+1, ans)
		fout.WriteString(s)
	}
}