diff --git a/examples/maths/numerical_integration/gaussian_legendre.f90 b/examples/maths/numerical_integration/gaussian_legendre.f90
index c85c9c4..e510724 100644
--- a/examples/maths/numerical_integration/gaussian_legendre.f90
+++ b/examples/maths/numerical_integration/gaussian_legendre.f90
@@ -22,7 +22,7 @@ program example_gaussian_quadrature
     ! Call Gaussian quadrature to compute the integral
     call gauss_legendre_quadrature(integral_result, a, b, n, func)
 
-    write(*, '(A, F12.6)') "Gaussian Quadrature result: ", integral_result          !! ≈ 0.858574
+    write (*, '(A, F12.6)') "Gaussian Quadrature result: ", integral_result          !! ≈ 0.858574
 
 contains
 
@@ -31,7 +31,7 @@ function func(x) result(fx)
         real(dp), intent(in) :: x
         real(dp) :: fx
 
-        fx = exp(-x**2) * cos(2.0_dp * x)       !! Example function to integrate
+        fx = exp(-x**2)*cos(2.0_dp * x)       !! Example function to integrate
     end function func
 
 end program example_gaussian_quadrature
\ No newline at end of file
diff --git a/examples/maths/numerical_integration/midpoint.f90 b/examples/maths/numerical_integration/midpoint.f90
index 3869da4..4e4ac56 100644
--- a/examples/maths/numerical_integration/midpoint.f90
+++ b/examples/maths/numerical_integration/midpoint.f90
@@ -21,7 +21,7 @@ program example_midpoint
     ! Call the midpoint rule subroutine with the function passed as an argument
     call midpoint(integral_result, a, b, n, func)
 
-    write(*, '(A, F12.6)') "Midpoint rule yields: ", integral_result  !! ≈ 0.858196
+    write (*, '(A, F12.6)') "Midpoint rule yields: ", integral_result  !! ≈ 0.858196
 
 contains
 
@@ -30,7 +30,7 @@ function func(x) result(fx)
         real(dp), intent(in) :: x
         real(dp) :: fx
 
-        fx = exp(-x**2) * cos(2.0_dp * x)       !! Example function to integrate
+        fx = exp(-x**2)*cos(2.0_dp * x)       !! Example function to integrate
     end function func
 
 end program example_midpoint
diff --git a/examples/maths/numerical_integration/monte_carlo.f90 b/examples/maths/numerical_integration/monte_carlo.f90
index 31cebbc..15423a0 100644
--- a/examples/maths/numerical_integration/monte_carlo.f90
+++ b/examples/maths/numerical_integration/monte_carlo.f90
@@ -22,7 +22,7 @@ program example_monte_carlo
     ! Call Monte Carlo integration
     call monte_carlo(integral_result, error_estimate, a, b, n, func)
 
-    write(*, '(A, F12.6, A, F12.6)') "Monte Carlo result: ", integral_result, " +- ", error_estimate     !! ≈ 0.858421
+    write (*, '(A, F12.6, A, F12.6)') "Monte Carlo result: ", integral_result, " +- ", error_estimate     !! ≈ 0.858421
 
 contains
 
diff --git a/examples/maths/numerical_integration/simpson.f90 b/examples/maths/numerical_integration/simpson.f90
index 4b7a437..7fdaefc 100644
--- a/examples/maths/numerical_integration/simpson.f90
+++ b/examples/maths/numerical_integration/simpson.f90
@@ -22,7 +22,7 @@ program example_simpson
     ! Call Simpson's rule with the function passed as an argument
     call simpson(integral_result, a, b, n, func)
 
-    write(*, '(A, F12.8)') "Simpson's rule yields: ", integral_result       !! ≈ 0.85819555
+    write (*, '(A, F12.8)') "Simpson's rule yields: ", integral_result       !! ≈ 0.85819555
 
 contains
 
@@ -31,7 +31,7 @@ function func(x) result(fx)
         real(dp), intent(in) :: x
         real(dp) :: fx
 
-        fx = exp(-x**2) * cos(2.0_dp * x)       !! Example function to integrate
+        fx = exp(-x**2)*cos(2.0_dp * x)       !! Example function to integrate
     end function func
 
 end program example_simpson
diff --git a/examples/maths/numerical_integration/trapezoid.f90 b/examples/maths/numerical_integration/trapezoid.f90
index 5c08c14..b46854d 100644
--- a/examples/maths/numerical_integration/trapezoid.f90
+++ b/examples/maths/numerical_integration/trapezoid.f90
@@ -22,7 +22,7 @@ program example_tapezoid
     ! Call the trapezoidal rule with the function passed as an argument
     call trapezoid(integral_result, a, b, n, func)
 
-    write(*, '(A, F12.6)') 'Trapezoidal rule yields: ', integral_result     !! ≈ 0.858195
+    write (*, '(A, F12.6)') 'Trapezoidal rule yields: ', integral_result     !! ≈ 0.858195
 
 contains
 
@@ -31,7 +31,7 @@ function func(x) result(fx)
         real(dp), intent(in) :: x
         real(dp) :: fx
 
-        fx = exp(-x**2) * cos(2.0_dp * x)       !! Example function to integrate
+        fx = exp(-x**2)*cos(2.0_dp * x)       !! Example function to integrate
     end function func
 
 end program example_tapezoid
diff --git a/modules/maths/numerical_integration/gaussian_legendre.f90 b/modules/maths/numerical_integration/gaussian_legendre.f90
index bc4c678..5f288bb 100644
--- a/modules/maths/numerical_integration/gaussian_legendre.f90
+++ b/modules/maths/numerical_integration/gaussian_legendre.f90
@@ -49,10 +49,10 @@ end function func
         call gauss_legendre_weights(t, w, n)
 
         ! Allocate the function value array
-        allocate(fx(n))
+        allocate (fx(n))
 
         ! Transform the nodes from the reference interval [-1, 1] to [a, b]
-        x = (b + a) / 2.0_dp + (b - a) * t / 2.0_dp
+        x = (b + a)/2.0_dp + (b - a)*t/2.0_dp
 
         ! Compute function values at the transformed points
         do i = 1, n
@@ -60,10 +60,10 @@ end function func
         end do
 
         ! Apply the Gaussian-Legendre quadrature formula
-        integral_result = sum(w * fx) * (b - a) / 2.0_dp
+        integral_result = sum(w*fx)*(b - a)/2.0_dp
 
         ! Deallocate fx array
-        deallocate(fx)
+        deallocate (fx)
 
     end subroutine gauss_legendre_quadrature
 
@@ -74,7 +74,7 @@ subroutine gauss_legendre_weights(t, w, n)
         real(dp), intent(out), dimension(n) :: t, w  !! Nodes (t) and weights (w)
 
         ! Predefined nodes and weights for different values of n
-        select case(n)
+        select case (n)
         case (1)
             t = [0.0_dp]        !! Single node at the center for n = 1
             w = [2.0_dp]        !! Weight of 2 for the single point
diff --git a/modules/maths/numerical_integration/midpoint.f90 b/modules/maths/numerical_integration/midpoint.f90
index 2612851..85d82e4 100644
--- a/modules/maths/numerical_integration/midpoint.f90
+++ b/modules/maths/numerical_integration/midpoint.f90
@@ -41,13 +41,13 @@ end function func
         end interface
 
         ! Step size
-        h = (b - a) / (1.0_dp*n)
+        h = (b - a)/(1.0_dp*n)
 
         ! Allocate array for midpoints
-        allocate(x(1:n), fx(1:n))
+        allocate (x(1:n), fx(1:n))
 
         ! Calculate midpoints
-        x = [(a + (i - 0.5_dp) * h, i = 1, n)]
+        x = [(a + (i - 0.5_dp)*h, i=1, n)]
 
         ! Apply function to each midpoint
         do i = 1, n
@@ -55,10 +55,10 @@ end function func
         end do
 
         ! Final integral value
-        integral_result = h * sum(fx)
+        integral_result = h*sum(fx)
 
         ! Deallocate arrays
-        deallocate(x, fx)
+        deallocate (x, fx)
 
     end subroutine midpoint
 
diff --git a/modules/maths/numerical_integration/monte_carlo.f90 b/modules/maths/numerical_integration/monte_carlo.f90
index 8563e8c..8856180 100644
--- a/modules/maths/numerical_integration/monte_carlo.f90
+++ b/modules/maths/numerical_integration/monte_carlo.f90
@@ -43,11 +43,11 @@ end function func
         end interface
 
         ! Allocate arrays for random samples and function values
-        allocate(uniform_sample(1:n), fx(1:n))
+        allocate (uniform_sample(1:n), fx(1:n))
 
         ! Generate uniform random points in [a, b]
         call random_number(uniform_sample)
-        uniform_sample = a + (b - a) * uniform_sample  !! Scale to the interval [a, b]
+        uniform_sample = a + (b - a)*uniform_sample  !! Scale to the interval [a, b]
 
         ! Evaluate the function at all random points in parallel
         !$omp parallel do           !! OpenMP parallelization to distribute the loop across multiple threads
@@ -61,13 +61,13 @@ end function func
         sum_fx_squared = sum(fx**2)
 
         ! Compute the Monte Carlo estimate of the integral
-        integral_result = (b - a) * (sum_fx / real(n, dp))
+        integral_result = (b - a)*(sum_fx/real(n, dp))
 
         ! Estimate the error using the variance of the function values
-        error_estimate = sqrt((sum_fx_squared/n - (sum_fx/n)**2) / (n-1)) * (b-a)
+        error_estimate = sqrt((sum_fx_squared/n - (sum_fx/n)**2)/(n - 1))*(b - a)
 
         ! Deallocate arrays
-        deallocate(uniform_sample, fx)
+        deallocate (uniform_sample, fx)
 
     end subroutine monte_carlo
 
diff --git a/modules/maths/numerical_integration/simpson.f90 b/modules/maths/numerical_integration/simpson.f90
index 1e2052a..a65b3d2 100644
--- a/modules/maths/numerical_integration/simpson.f90
+++ b/modules/maths/numerical_integration/simpson.f90
@@ -44,18 +44,18 @@ end function func
 
         ! Check if n is even
         if (mod(n, 2) /= 0) then
-            write(*, *) 'Error: The number of panels (n) must be even.'
+            write (*, *) 'Error: The number of panels (n) must be even.'
             stop
         end if
 
         ! Step size
-        h = (b - a) / (1.0_dp*n)
+        h = (b - a)/(1.0_dp*n)
 
         ! Allocate arrays
-        allocate(x(0:n), fx(0:n))
+        allocate (x(0:n), fx(0:n))
 
         ! Create an array of x values, contains the endpoints and the midpoints.
-        x = [(a + i * h, i = 0, n)]
+        x = [(a + i*h, i=0, n)]
 
         ! Apply the function to each x value
         do i = 0, n
@@ -63,10 +63,10 @@ end function func
         end do
 
         ! Apply Simpson's rule using array slicing
-        integral_result = (fx(0) + fx(n) + 4.0_dp * sum(fx(1: n-1: 2)) + 2.0_dp * sum(fx(2: n-2: 2))) * (h / 3.0_dp)
+        integral_result = (fx(0) + fx(n) + 4.0_dp*sum(fx(1:n - 1:2)) + 2.0_dp*sum(fx(2:n - 2:2)))*(h/3.0_dp)
 
         ! Deallocate arrays
-        deallocate(x, fx)
+        deallocate (x, fx)
     end subroutine simpson
 
 end module simpson_rule
diff --git a/modules/maths/numerical_integration/trapezoid.f90 b/modules/maths/numerical_integration/trapezoid.f90
index f2f3a11..8f13d7c 100644
--- a/modules/maths/numerical_integration/trapezoid.f90
+++ b/modules/maths/numerical_integration/trapezoid.f90
@@ -42,13 +42,13 @@ end function func
         end interface
 
         ! Step size
-        h = (b - a) / (1.0_dp*n)
+        h = (b - a)/(1.0_dp*n)
 
         ! Allocate arrays
-        allocate(x(0:n), fx(0:n))
+        allocate (x(0:n), fx(0:n))
 
         ! Create an array of x values
-        x = [(a + i * h, i = 0, n)]
+        x = [(a + i*h, i=0, n)]
 
         ! Apply the function to each x value
         do i = 0, n
@@ -56,10 +56,10 @@ end function func
         end do
 
         ! Apply trapezoidal rule using array slicing
-        integral_result = ((fx(0) + fx(n)) * 0.5_dp + sum(fx(1: n))) * h
+        integral_result = ((fx(0) + fx(n))*0.5_dp + sum(fx(1:n)))*h
 
         ! Deallocate arrays
-        deallocate(x, fx)
+        deallocate (x, fx)
     end subroutine trapezoid
 
 end module trapezoidal_rule