# CalculusApi

This code defines a Flask application that serves as an API for performing integration and differentiation. The API has two endpoints, `/integration` and `/differentiation`, that can be accessed using a POST request.

# Contribute to this API freely by creating a pull request.
 
## Lists of Features 
The integration endpoint expects a JSON object in the request body with the following properties:

+ function1: a string representing the mathematical function to be integrated
lower: a numeric value representing the lower bound of the integration
upper: a numeric value representing the upper bound of the integration
The differentiation endpoint expects a JSON object in the request body with the following properties:

- function2: a string representing the mathematical function to be differentiated
point: a numeric value representing the point at which the derivative should be calculated
Both endpoints use a pre-trained model, which is loaded at the beginning of the script using the keras.models.load_model function. The model is expected to be saved in a file named `model.h5` in the same directory as the script.

The integration and differentiation functions use the predict method of the model to obtain the definite integral and derivative of a function. They then return the result in the form of a string, which is the response of the API.

The script starts the Flask application if the script is run as the main module.

You need to make sure that your dataset and model are trained properly and saved in `"model.h5"` at the same directory of the script. Also, you need to check that the dataset of your trained model corresponds to the input data of the integration and differentiation endpoints of the API.

# Model Scripts

This script is a basic example of how to train a model using TensorFlow and the Keras API. Here's an overview of what the script does:

+ Imports necessary modules: The script imports `TensorFlow`, the `Keras API`, and `Numpy`.

+ Load the dataset: The script uses the built-in Boston Housing dataset, which is included in the Keras library. It loads the dataset into training and testing sets.

- Scale the input data: The script normalizes the input data by dividing each value by the maximum value in the dataset. This is done to ensure that all the input data is in the same range and helps with the training process.

+ Define the model: The script creates a Sequential model and adds two Dense layers to the model. The first layer has 13 neurons and the second has 1 neuron. The first layer is the input layer and the second is the output layer.

- Compile the model: The script compiles the model by specifying the optimizer (Adam) and the loss function (mean squared error)

+ Train the model: The script trains the model using the x_train and y_train data, and runs it for 100 epochs

+ Evaluate the model: The script evaluates the model by using the x_test and y_test data and prints the test loss.

+ Save the model: The script saves the trained model to a file named "model.h5"

This script is a basic example of how to train a model using the Boston Housing dataset and it is not related to integration and differentiation. In order to train a model that can handle integration and differentiation, you will need a more comprehensive dataset and also need to handle the symbolic math expressions and also need to integrate the model with the flask API.

# Train the Model

Here are some steps you can take to learn how to train a h5 model with two given datasets, and run the above API:

Learn about TensorFlow and the Keras API: TensorFlow is an open-source machine learning library and the Keras API is a high-level interface for building and training models with TensorFlow. Start by learning the basics of TensorFlow and the Keras API, including how to create and train models, and how to save and load models.

Learn about h5 file format: h5 file format is used to store large amounts of numerical data. It is designed for fast access and low memory usage, and is widely used in machine learning and deep learning. Learn about how h5 files are structured and how to read and write data to h5 files using the h5py library.

Learn about splitting and preprocessing datasets: Before training a model, it's important to split your dataset into training and testing sets, and preprocess the data so that it can be used to train a model. Learn about different methods for splitting datasets and different techniques for preprocessing data.

Learn about model evaluation: After training a model, it's important to evaluate its performance on the test set. Learn about different metrics and techniques for evaluating the performance of a model, such as accuracy and mean squared error.

Practice: Once you've learned the basics, practice building and training models with the two given datasets. Experiment with different model architectures and different preprocessing techniques to see how they affect the model's performance.

Learn about Flask: Flask is a micro web framework written in Python. It is classified as a microframework because it does not require particular tools or libraries. It has no database abstraction layer, form validation, or any other components where pre-existing third-party libraries provide common functions. Learn how to create a basic Flask application, how to handle GET and POST requests, how to send and receive JSON data, and how to run a Flask application.

Integrate the model and the API: Once you've learned how to train the h5 model and how to create a basic Flask API, integrate the two to create the final API that will receive the requests, parse the data, make predictions using the model, and return the results.

It's also worth noting that, training a model for integration and differentiation is a very complex task and requires a large amount of data and a very powerful machine learning model to achieve good results. It's also important to note that, the accuracy of the model will depend on the quality of the dataset and the complexity of the functions that you are trying to integrate or differentiate.

The example code I provided earlier was for training a model to predict the median value of owner-occupied homes in the Boston area using the Boston Housing dataset. It is not specific to integration and differentiation.

To train a model for integration and differentiation, you would need a dataset that includes function expressions and the corresponding definite integral or derivative values. The dataset could be in the form of a CSV file or a set of arrays.

Here's an example of how you might create a dataset for integration and differentiation:

```
import numpy as np

# Create a list of function expressions
functions = ['x**2', 'sin(x)', 'e**x', '1/x']

# Create a list of lower bounds
lowers = [-1, -2, 0, 1]

# Create a list of upper bounds
uppers = [1, 2, 3, 2]

# Create a list of definite integral values
integrals = [1/3, -cos(2), (e**3 - 1), ln(2)]

# Combine the lists into a dataset
dataset = np.column_stack((functions, lowers, uppers, integrals))
Similarly, you can create a dataset for differentiation:
```

```` 
import numpy as np

# Create a list of function expressions
functions = ['x**2', 'sin(x)', 'e**x', '1/x']

# Create a list of points
points = [-1, 0, 1, 2]

# Create a list of derivative values
derivatives = [2*x, cos(x), e**x, -1/x**2]

# Combine the lists into a dataset
dataset = np.column_stack((functions, points, derivatives))
