#        
## Overview

**SciPy** is an open-source library provided by Python dedicated to scientific computation. The **`scipy.integrate`** is a sub-package that provides the functionality to solve several integration methods, including Ordinary Differential Equations (ODEs). The **`scipy.integrate.tplquad`** method in SciPy is used to solve general-purpose triple integration. 


## Syntax

```Python
scipy.integrate.tplquad(func, a, b, gfun, hfun, qfun, rfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)
``` 

## Parameters

* `func`: A Python function or method representing a double integral function taking at least two inputs that act as variables to the double integral. It should take inputs in the variable order: $z,y,x$

* `a,b`: The integration limits in $x$ where $a<b$. Both have the type `float`.
* `gfun`: A python function or a `float` representing the lower boundary curve in $y$, a function of $x$ and returns a single floating-point value.

* `hfun`: A python function or a `float` representing the higher boundary curve in $y$, a function of $x$ and returns a single floating-point value.

* `qfun`: A python function or a `float` representing the lower boundary surface in $z$, a function of $x,y$ in that order and returns a single floating-point value.
* `rfun`: A python function or a `float` representing the upper boundary surface in $z$, a function of $x,y$ in that order and returns a single floating-point value. 

* `args`: An optional parameter which is a sequence of extra arguments passed to `func`.

* `epsabs`: An optional parameter that is the absolute tolerance passed directly to the inner 1-D quadrature integration. Default is $1.49e-8$.

* `epsrel`: An optional parameter that is the relative tolerance of the inner 1-D integrals. Default is $1.49e-8$.

## Return value

- `y`: The computed double definite integral of `func(y,x)`. It has the type `float`.

- `abserr`: An estimate of the error. It has the type `float`.


## Code

Lets see how to compute the triple intergal of $f(z,y,x) = xyz^4$ using the `scipy.integrate.tplquad` method where $x$ is ranging from $1$ to $2$, $y$ is ranging from $2$ to $3$, and $z$ is ranging from $0$ to $1$.



from scipy import integrate
func = lambda z, y, x: x*y*z**4
print(integrate.tplquad(func, 1, 2, lambda x: 2, lambda x: 3,
                  lambda x, y: 0, lambda x, y: 1))

# Explanation
* **Line 2**: We write the lambda function `func` which takes input in the order `z,y,x`.

* **Line 3**: We use the `scipy.integrate.tplquad` method that returns the triple (definite) integral of `func`. The result is then printed.

> **Note**: `gfun` and `hfun` are constant boundary curves in $y$ as a lambda function of `x`. And `qfun` and `rfun` are the boundary surface in $z$ as a lambda function of `y` and `x`.

What is the scipy.integrate.tplquad method?

SciPy’s `tplquad` method for triple integration functions with defined parameter limits. Example: `λ` function for `xyz^4` over specified ranges.