Here is the sample output: Example Output for the Final Project Assignment

$$ LaFleur MENU

$--------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $1$

The Simpson's Rule is $32\mathrm{.}38935202589829$

$$ LaFleur MENU

$-------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $2$

Integral Estimate Using Trap Unequally Spaced Data $=28\mathrm{.}01000$

Cubic fitted polynomial coefficients:

$[0\mathrm{.}08396376-0\mathrm{.}68664788-0\mathrm{.}619979456\mathrm{.}71060393]$

Integration of cubic polynomial $=10\mathrm{.}41$

Average EDR $=5\mathrm{.}394$

Evaluation of of cubic polynomial using numpy eval $=-0\mathrm{.}27081429023614145$

$$ LaFleur MENU

$--------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $3$

$***************************************$

LaFleurs Integration Method Using The Trap Function

The Trap Rule is $2\mathrm{.}535703439355347$

$$ LaFleur MENU

$--------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $4$

The Interpolation of an ECG$-$derived respiration $($EDR$)$ rate in mV$($millivolt$)$

Using Cubic Spline Is $-45\mathrm{.}7503830937899$

$$ LaFleur MENU

$--------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $5$

Lagrange Output is $-35\mathrm{.}78682397745067$

$$ LaFleur MENU

$--------------------------------------------------------$

$1-$ LaFleur Simpson$\_$Rule

$2-$ LaFleur Trap Unequally Spaced Data

$3-$ LaFleur Function Integration Method Using Trap

$4-$ LaFLeur Cubic Spline Interpolation

$5-$ laFleur Lagrange Polynomial Interpolation

$6-$ EXIT

Enter your choice: $6$

Here is the CSV data file to be used:

$0\mathrm{.}014-50$

$0\mathrm{.}21819$

$0\mathrm{.}416-20$

$0\mathrm{.}61526$

$0\mathrm{.}81636$

$1\mathrm{.}00931$

$1\mathrm{.}19837$

$1\mathrm{.}38312$

$1\mathrm{.}567-19$

$1\mathrm{.}74913$

$1\mathrm{.}93622$

$2\mathrm{.}1260$

$2\mathrm{.}316-52$

$2\mathrm{.}51-4$

$2\mathrm{.}70536$

$2\mathrm{.}90434$

$3\mathrm{.}102-28$

$3\mathrm{.}301-19$

$3\mathrm{.}511$

$3\mathrm{.}7011$

$3\mathrm{.}89976$

$4\mathrm{.}09868$

$4\mathrm{.}296-54$

$4\mathrm{.}496-42$

$4\mathrm{.}7-59$

$4\mathrm{.}908-63$

$5\mathrm{.}115-51$

$5\mathrm{.}323-66$

$5\mathrm{.}5329$

$5\mathrm{.}74246$

$5\mathrm{.}95470$

$6\mathrm{.}16641$

$6\mathrm{.}38221$

$6\mathrm{.}613$

$6\mathrm{.}81-100$

$7\mathrm{.}015-42$

$7\mathrm{.}218-13$

$7\mathrm{.}415-13$

$7\mathrm{.}61364$

$7\mathrm{.}811-12$

$8\mathrm{.}00412$

$8\mathrm{.}19259$

$8\mathrm{.}37723$

$8\mathrm{.}566-46$

$8\mathrm{.}75973$

$8\mathrm{.}9598$

$9\mathrm{.}163-117$

$9\mathrm{.}36977$

$9\mathrm{.}572102$

$9\mathrm{.}779-87$