Calculate the Integral

Time Limit: 2 Seconds
Memory Limit: 65536 KB

Define the following functions:

Given integer N (1 <= n <= 100) and {an} {bn}, for 1 <= i <= N,
define:

and

calculate the integral:

**Input**

A line containing only the integer N is given first.

Then N lines follow, each line has two float-point number Ai and Bi.

There are several test cases, so process to the end of file.

**Output**

For each testcase, output a line containing only the integer N first.

Then output a second line containing the result of the integral.

The result should be printed in scientific format which has a precision of 10
digits after radix point.

**Sample Input**

1

0 2

2

1 3

0 4

3

2 4

1 5

0 6

**Sample Output**

1

0.0000000000e+000

2

8.0000000000e+000

3

7.2000000000e+001

Author:

**SHI, Xiaohan**
Source:

**ZOJ Monthly, May 2003**
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